https://drorbn.net/index.php?action=history&feed=atom&title=10-327%2FHomework_Assignment_7 2026-06-19T01:39:48Z Revision history for this page on the wiki MediaWiki 1.39.6 https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10334&oldid=prev 2010-12-11T02:56:59Z

<p>EDIT: moved Kai&#039;s HW7 solutions to new page</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:56, 10 December 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 27:</td> <td colspan="2" class="diff-lineno">Line 27:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Yes, &lt;math&gt;J&lt;/math&gt; is arbitrary and &lt;math&gt;A&lt;/math&gt; is closed. [[User:Drorbn|Drorbn]] 06:41, 22 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Yes, &lt;math&gt;J&lt;/math&gt; is arbitrary and &lt;math&gt;A&lt;/math&gt; is closed. [[User:Drorbn|Drorbn]] 06:41, 22 November 2010 (EST)</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===Solution===</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Here is the solution to HW7. -Kai</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/b/b2/10-327a701_%281%29.JPG page1]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/3/30/10-327a701_%282%29.JPG page2]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/a/ac/10-327a701_%283%29.JPG page3]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/7/77/10-327a701_%284%29.JPG page4]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/4/40/10-327a701_%285%29.JPG page5]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/d/db/10-327a701_%286%29.JPG page6]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/e/ef/10-327a701_%287%29.JPG page7]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/6/66/10-327a701_%288%29.JPG page8]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/7/71/10-327a701_%289%29.JPG page9]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; 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Anne.d https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10277&oldid=prev 2010-12-04T18:16:33Z

<p><span dir="auto"><span class="autocomment">Solution</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:16, 4 December 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 31:</td> <td colspan="2" class="diff-lineno">Line 31:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Here is the solution to HW7. -Kai</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Here is the solution to HW7. -Kai</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/b/b2/10-327a701_%281%29.JPG page1]</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/b/b2/10-327a701_%281%29.JPG page1]</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; 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Xwbdsb https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10276&oldid=prev 2010-12-04T18:14:13Z

<p><span dir="auto"><span class="autocomment">Due date</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:14, 4 December 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 27:</td> <td colspan="2" class="diff-lineno">Line 27:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Yes, &lt;math&gt;J&lt;/math&gt; is arbitrary and &lt;math&gt;A&lt;/math&gt; is closed. [[User:Drorbn|Drorbn]] 06:41, 22 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Yes, &lt;math&gt;J&lt;/math&gt; is arbitrary and &lt;math&gt;A&lt;/math&gt; is closed. [[User:Drorbn|Drorbn]] 06:41, 22 November 2010 (EST)</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===Solution===</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Here is the solution to HW7. -Kai</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/b/b2/10-327a701_%281%29.JPG page1]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/7/7e/10-327a502.JPG page2]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/6/6b/10-327a503.JPG page3]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/6/61/10-327a504.JPG page4]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/1/1d/10-327a505.JPG page5]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/c/c6/10-327a506.JPG page6]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/7/77/10-327a507.JPG page7]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/d/df/10-327a508.JPG page8]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/9/9d/10-327a509.JPG page9]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/8/8e/10-327a510.JPG page10]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/7/75/10-327a511.JPG page11]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/7/70/10-327a512.JPG page12]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/d/dc/10-327a513.JPG page13]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/4/4d/10-327a514.JPG page14]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/c/c5/10-327a515.JPG page15]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/6/6d/10-327a516.JPG page16]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/c/c6/10-327a517.JPG page17]</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[http://katlas.math.toronto.edu/drorbn/images/d/d5/10-327a518.JPG page18]</div></td> </tr> <!-- diff cache key drordb-drorbn_:diff:wikidiff2:1.12:old-10163:rev-10276:1.13.0 --> </table>

Xwbdsb https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10163&oldid=prev 2010-11-22T11:41:03Z

<p><span dir="auto"><span class="autocomment">Due date</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:41, 22 November 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 26:</td> <td colspan="2" class="diff-lineno">Line 26:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>** Yes, &lt;math&gt;J&lt;/math&gt; is arbitrary and &lt;math&gt;A&lt;/math&gt; is closed. [[User:Drorbn|Drorbn]] 06:41, 22 November 2010 (EST)</div></td> </tr> <!-- diff cache key drordb-drorbn_:diff:wikidiff2:1.12:old-10161:rev-10163:1.13.0 --> </table>

Drorbn https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10161&oldid=prev 2010-11-22T03:32:34Z

<p><span dir="auto"><span class="autocomment">Due date</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:32, 21 November 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 23:</td> <td colspan="2" class="diff-lineno">Line 23:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question. If we have a finite set of continuous function mapping from any topological space into the reals. Any linear combination of these continuous function is still continuous right? The proof is a little extension of 157 proof. This is used to prove the statement you mentioned above. -Kai[[User:Xwbdsb|Xwbdsb]] 17:14, 20 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question. If we have a finite set of continuous function mapping from any topological space into the reals. Any linear combination of these continuous function is still continuous right? The proof is a little extension of 157 proof. This is used to prove the statement you mentioned above. -Kai[[User:Xwbdsb|Xwbdsb]] 17:14, 20 November 2010 (EST)</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>** Any linear combination of functions from &lt;math&gt;\mathcal{C}(X,\mathbb{R})&lt;/math&gt; (an uncountable set unless X is empty) is continuous. On its own, however, this proves nothing about infinite sums. [[User:Bcd|Bcd]] 22:32, 21 November 2010 (EST)</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> </tr> <!-- diff cache key drordb-drorbn_:diff:wikidiff2:1.12:old-10160:rev-10161:1.13.0 --> </table>

Bcd https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10160&oldid=prev 2010-11-21T03:13:00Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:13, 20 November 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 23:</td> <td colspan="2" class="diff-lineno">Line 23:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question. If we have a finite set of continuous function mapping from any topological space into the reals. Any linear combination of these continuous function is still continuous right? The proof is a little extension of 157 proof. This is used to prove the statement you mentioned above. -Kai[[User:Xwbdsb|Xwbdsb]] 17:14, 20 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Question. If we have a finite set of continuous function mapping from any topological space into the reals. Any linear combination of these continuous function is still continuous right? The proof is a little extension of 157 proof. This is used to prove the statement you mentioned above. -Kai[[User:Xwbdsb|Xwbdsb]] 17:14, 20 November 2010 (EST)</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Question about 9. Is J any indexing set? Possibly uncountable? in the hint: A means any closed set? -Kai [[User:Xwbdsb|Xwbdsb]] 22:13, 20 November 2010 (EST)</div></td> </tr> </table>

Xwbdsb https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10159&oldid=prev 2010-11-20T22:14:33Z

<p><span dir="auto"><span class="autocomment">Due date</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:14, 20 November 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 21:</td> <td colspan="2" class="diff-lineno">Line 21:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Questions by Kai [[User:Xwbdsb|Xwbdsb]] 21:26, 19 November 2010 (EST) were moved to [[10-327/Classnotes for Thursday November 18|Classnotes for Thursday November 18]] as they are about that class and not about this assignment. [[User:Drorbn|Drorbn]] 06:03, 20 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Questions by Kai [[User:Xwbdsb|Xwbdsb]] 21:26, 19 November 2010 (EST) were moved to [[10-327/Classnotes for Thursday November 18|Classnotes for Thursday November 18]] as they are about that class and not about this assignment. [[User:Drorbn|Drorbn]] 06:03, 20 November 2010 (EST)</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Question. If we have a finite set of continuous function mapping from any topological space into the reals. Any linear combination of these continuous function is still continuous right? The proof is a little extension of 157 proof. This is used to prove the statement you mentioned above. -Kai[[User:Xwbdsb|Xwbdsb]] 17:14, 20 November 2010 (EST)</div></td> </tr> <!-- diff cache key drordb-drorbn_:diff:wikidiff2:1.12:old-10151:rev-10159:1.13.0 --> </table>

Xwbdsb https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10151&oldid=prev 2010-11-20T11:04:09Z

<p><span dir="auto"><span class="autocomment">Due date</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:04, 20 November 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 20:</td> <td colspan="2" class="diff-lineno">Line 20:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Questions by Kai [[User:Xwbdsb|Xwbdsb]] 21:26, 19 November 2010 (EST) were <del style="font-weight: bold; text-decoration: none;">move</del> to [[10-327/Classnotes for Thursday November 18|Classnotes for Thursday November 18]] as they are about that class and not about this assignment. [[User:Drorbn|Drorbn]] 06:03, 20 November 2010 (EST)</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Questions by Kai [[User:Xwbdsb|Xwbdsb]] 21:26, 19 November 2010 (EST) were <ins style="font-weight: bold; text-decoration: none;">moved</ins> to [[10-327/Classnotes for Thursday November 18|Classnotes for Thursday November 18]] as they are about that class and not about this assignment. [[User:Drorbn|Drorbn]] 06:03, 20 November 2010 (EST)</div></td> </tr> <!-- diff cache key drordb-drorbn_:diff:wikidiff2:1.12:old-10150:rev-10151:1.13.0 --> </table>

Drorbn https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10150&oldid=prev 2010-11-20T11:03:49Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:03, 20 November 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 20:</td> <td colspan="2" class="diff-lineno">Line 20:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Questions by Kai [[User:Xwbdsb|Xwbdsb]] 21:26, 19 November 2010 (EST):</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Questions by Kai [[User:Xwbdsb|Xwbdsb]] 21:26, 19 November 2010 (EST)<ins style="font-weight: bold; text-decoration: none;"> were move to [[10-327/Classnotes for Thursday November 18|Classnotes for Thursday November 18]] as they are about that class and not about this assignment. [[User</ins>:<ins style="font-weight: bold; text-decoration: none;">Drorbn|Drorbn]] 06:03, 20 November 2010 (EST)</ins></div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># I have concern about this "Adding T_1 thing". When we are proving the Urysohn's Lemma, we proved that if X is a T.S. and A,B are any two disjoint closed sets in X, they can be separated by two disjoint open sets in X iff they can be separated by a continuous function. So there is no T_1 axiom involved in any of these two proofs. So Urysohn's Lemma is something more general than T_4 iff T_4.5 right? </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># I just want to also confirm the definition of T_4 and T_4.5: T_4 is T_1 + separation by two disjoint open sets for any two disjoint closed sets and T_4.5 is T_1 + separation by a continuous function for any two disjoint closed sets?</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># The only purpose of this manually adding T_1 thing is that so that T_4 and T_4.5 could imply T_3 T_2 T_1 right?</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Dror you said before that induction can go up to finite n but why in this case induction will work for a countably infinite set of elements?</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> </table>

Drorbn https://drorbn.net/index.php?title=10-327/Homework_Assignment_7&diff=10148&oldid=prev 2010-11-20T10:52:31Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 06:52, 20 November 2010</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 19:</td> <td colspan="2" class="diff-lineno">Line 19:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Yes. [[User:Drorbn|Drorbn]] 19:14, 19 November 2010 (EST)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>** Yes. [[User:Drorbn|Drorbn]] 19:14, 19 November 2010 (EST)</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>----</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Questions: </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_12_5_lhs">&#x26AB;</a></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><a name="movedpara_3_0_rhs"></a><ins style="font-weight: bold; text-decoration: none;">Questions by </ins>Kai<ins style="font-weight: bold; text-decoration: none;"> </ins>[[User:Xwbdsb|Xwbdsb]] 21:26, 19 November 2010 (EST)<ins style="font-weight: bold; text-decoration: none;">:</ins></div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">(1)</del>I have concern about this "Adding T_1 thing". When we are proving the Urysohn's Lemma, we proved that if X is a T.S. and A,B are any two disjoint closed sets in X, they can be separated by two disjoint open sets in X iff they can be separated by a continuous function. So there is no T_1 axiom involved in any of these two proofs. So Urysohn's Lemma is something more general than T_4 iff T_4.5 right? </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"># </ins>I have concern about this "Adding T_1 thing". When we are proving the Urysohn's Lemma, we proved that if X is a T.S. and A,B are any two disjoint closed sets in X, they can be separated by two disjoint open sets in X iff they can be separated by a continuous function. So there is no T_1 axiom involved in any of these two proofs. So Urysohn's Lemma is something more general than T_4 iff T_4.5 right? </div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_9_0_lhs">&#x26AB;</a></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><a name="movedpara_6_0_rhs"></a><ins style="font-weight: bold; text-decoration: none;"># </ins>I just want to also confirm the definition of T_4 and T_4.5: T_4 is T_1 + separation by two disjoint open sets for any two disjoint closed sets and T_4.5 is T_1 + separation by a continuous function for any two disjoint closed sets?</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_12_0_lhs">&#x26AB;</a></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><a name="movedpara_8_0_rhs"></a><ins style="font-weight: bold; text-decoration: none;"># </ins>The only purpose of this manually adding T_1 thing is that so that T_4 and T_4.5 could imply T_3 T_2 T_1 right?</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_6_0_rhs">&#x26AB;</a></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><a name="movedpara_9_0_lhs"></a><del style="font-weight: bold; text-decoration: none;">(2)</del>I just want to also confirm the definition of T_4 and T_4.5: T_4 is T_1 + separation by two disjoint open sets for any two disjoint closed sets and T_4.5 is T_1 + separation by a continuous function for any two disjoint closed sets?</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Paragraph was moved. Click to jump to old location." href="#movedpara_12_2_lhs">&#x26AB;</a></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><a name="movedpara_10_0_rhs"></a><ins style="font-weight: bold; text-decoration: none;"># </ins>Dror you said before that induction can go up to finite n but why in this case induction will work for a countably infinite set<ins style="font-weight: bold; text-decoration: none;"> of elements?</ins></div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_8_0_rhs">&#x26AB;</a></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><a name="movedpara_12_0_lhs"></a><del style="font-weight: bold; text-decoration: none;">(3)</del>The only purpose of this manually adding T_1 thing is that so that T_4 and T_4.5 could imply T_3 T_2 T_1 right?</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_10_0_rhs">&#x26AB;</a></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><a name="movedpara_12_2_lhs"></a><del style="font-weight: bold; text-decoration: none;">(4)</del>Dror you said before that induction can go up to finite n but why in this case induction will work for a countably infinite set</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>of elements?</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Paragraph was moved. Click to jump to new location." href="#movedpara_3_0_rhs">&#x26AB;</a></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><a name="movedpara_12_5_lhs"></a><del style="font-weight: bold; text-decoration: none;">-</del>Kai[[User:Xwbdsb|Xwbdsb]] 21:26, 19 November 2010 (EST)</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> </table>

Drorbn