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0708-1300/Homework Assignment 4 - Revision history
2026-05-05T05:29:28Z
Revision history for this page on the wiki
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https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5917&oldid=prev
Drorbn at 17:49, 19 November 2007
2007-11-19T17:49:21Z
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Drorbn
https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5913&oldid=prev
Franklin: /* Just for Fun */
2007-11-18T17:30:52Z
<p><span dir="auto"><span class="autocomment">Just for Fun</span></span></p>
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<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>Look at the story of [[0708-1300/Barnie the polar bear | Barnie the polar bear]].</div></td>
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<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>
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<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>If <math>n\neq m</math> then <math>{\mathbf R}^n</math> is [[0708-1300/not homeomorphic|not homeomorphic]] to <math>{\mathbf R}^m</math>.</div></td>
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<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>If <math>n\neq m</math> then <math>{\mathbf R}^n</math> is [[0708-1300/not homeomorphic|not homeomorphic]] to <math>{\mathbf R}^m</math>.</div></td>
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Franklin
https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5902&oldid=prev
Franklin: /* Just for Fun */
2007-11-18T17:15:18Z
<p><span dir="auto"><span class="autocomment">Just for Fun</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:15, 18 November 2007</td>
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<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>Look at the story of [[0708-1300/Barnie the polar bear | Barnie the polar bear]].</div></td>
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<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>Look at the story of [[0708-1300/Barnie the polar bear | Barnie the polar bear]].</div></td>
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<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>If <math>n\neq m</math> then <math>{\mathbf R}^n</math> is [[0708-1300/not homeomorphic<del style="font-weight: bold; text-decoration: none;"> </del>not homeomorphic]] to <math>{\mathbf R}^m</math>.</div></td>
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<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>If <math>n\neq m</math> then <math>{\mathbf R}^n</math> is [[0708-1300/not homeomorphic<ins style="font-weight: bold; text-decoration: none;">|</ins>not homeomorphic]] to <math>{\mathbf R}^m</math>.</div></td>
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Franklin
https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5901&oldid=prev
Franklin at 17:14, 18 November 2007
2007-11-18T17:14:49Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:14, 18 November 2007</td>
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<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>
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<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>Look at the story of [[0708-1300/Barnie the polar bear | Barnie the polar bear]].</div></td>
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<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>Look at the story of [[0708-1300/Barnie the polar bear | Barnie the polar bear]].</div></td>
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<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>If <math>n\neq m</math> then <math>{\mathbf R}^n</math> is [[0708-1300/not homeomorphic not homeomorphic]] to <math>{\mathbf R}^m</math>.</div></td>
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Franklin
https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5900&oldid=prev
Drorbn at 16:39, 18 November 2007
2007-11-18T16:39:34Z
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<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 6.'''</div></td>
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<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># Show that if <math>n\neq m</math> then <math>{\mathbf R}^n</math> is not diffeomorphic (homeomorphic via a smooth map with a smooth inverse) to <math>{\mathbf R}^m</math>.</div></td>
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<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># Show that if <math>n\neq m</math> then <math>{\mathbf R}^n</math> is not diffeomorphic (homeomorphic via a smooth map with a smooth inverse) to <math>{\mathbf R}^m</math>.</div></td>
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<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># Show that if <math>n\neq m</math> then <math>{\mathbf R}^n</math> is not homeomorphic to <math>{\mathbf R}^m</math>.</div></td>
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<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;"><strike></ins>Show that if <math>n\neq m</math> then <math>{\mathbf R}^n</math> is not homeomorphic to <math>{\mathbf R}^m</math>.<ins style="font-weight: bold; text-decoration: none;"></strike></ins></div></td>
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<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>Note that a priori the second part of this question is an order of magnitude harder than the first<del style="font-weight: bold; text-decoration: none;">,</del> <del style="font-weight: bold; text-decoration: none;">though</del> with <del style="font-weight: bold; text-decoration: none;">the</del> techniques <del style="font-weight: bold; text-decoration: none;">we</del> <del style="font-weight: bold; text-decoration: none;">already</del> <del style="font-weight: bold; text-decoration: none;">have,</del> it <del style="font-weight: bold; text-decoration: none;">is</del> <del style="font-weight: bold; text-decoration: none;">not</del> <del style="font-weight: bold; text-decoration: none;">too</del> <del style="font-weight: bold; text-decoration: none;">bad</del> <del style="font-weight: bold; text-decoration: none;">at</del> <del style="font-weight: bold; text-decoration: none;">all</del>.</div></td>
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<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>Note that a priori the second part of this question is an order of magnitude harder than the first<ins style="font-weight: bold; text-decoration: none;">.</ins> <ins style="font-weight: bold; text-decoration: none;">I am not sure how to do it</ins> with <ins style="font-weight: bold; text-decoration: none;">our current</ins> techniques<ins style="font-weight: bold; text-decoration: none;">,</ins> <ins style="font-weight: bold; text-decoration: none;">though</ins> <ins style="font-weight: bold; text-decoration: none;">later</ins> <ins style="font-weight: bold; text-decoration: none;">on</ins> it <ins style="font-weight: bold; text-decoration: none;">will</ins> <ins style="font-weight: bold; text-decoration: none;">become an easy</ins> <ins style="font-weight: bold; text-decoration: none;">consequence</ins> <ins style="font-weight: bold; text-decoration: none;">of</ins> <ins style="font-weight: bold; text-decoration: none;">"homology</ins> <ins style="font-weight: bold; text-decoration: none;">theory"</ins>.</div></td>
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Drorbn
https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5882&oldid=prev
Drorbn at 22:40, 8 November 2007
2007-11-08T22:40:19Z
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Drorbn
https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5822&oldid=prev
Drorbn at 14:51, 1 November 2007
2007-11-01T14:51:11Z
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Drorbn
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Drorbn at 14:48, 1 November 2007
2007-11-01T14:48:47Z
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Drorbn
https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5820&oldid=prev
Drorbn at 14:48, 1 November 2007
2007-11-01T14:48:10Z
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<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>Also, solve and submit the following question:</div></td>
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<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 6.'''</div></td>
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<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># Show that if <math>n\neq m</math> then <math>{\mathbf R}^n</math> is not diffeomorphic (homeomorphic via a smooth map with a smooth inverse) to <math>{\mathbf R}^m</math>.</div></td>
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<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># Show that if <math>n\neq m</math> then <math>{\mathbf R}^n</math> is not homeomorphic to <math>{\mathbf R}^m</math>.</div></td>
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Drorbn
https://drorbn.net/index.php?title=0708-1300/Homework_Assignment_4&diff=5818&oldid=prev
Drorbn at 14:11, 1 November 2007
2007-11-01T14:11:32Z
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<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>(Of course, you have to first obtain a ''geometric'' understanding of <math>[X,Y]</math>, and this in itself is significant and worthwhile).</div></td>
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<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>Look at the story of [[0708-1300/Barnie the polar bear | Barnie the polar bear]].</div></td>
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<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>Look at the story of [[0708-1300/Barnie the polar bear | Barnie the polar bear]].</div></td>
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Drorbn