10-327/Homework Assignment 2 - Revision history

Anne.d at 02:43, 12 November 2010

2010-11-12T02:43:37Z

← Older revision		Revision as of 22:43, 11 November 2010
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	*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)		*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)
	**** An arbitrary intersection of open sets is not necessarily open. This I'll say, but beyond this, it is your problem to solve. [[User:Drorbn\|Drorbn]] 16:21, 2 October 2010 (EDT)		**** An arbitrary intersection of open sets is not necessarily open. This I'll say, but beyond this, it is your problem to solve. [[User:Drorbn\|Drorbn]] 16:21, 2 October 2010 (EDT)

	===Solution===

	As promised, I provide my solution to HW2 here for any one of you might care. -Kai
	http://www.2shared.com/document/DVGaHsqO/HW2sol.html

	Also try this link if the previous one does not work.
	http://www.megaupload.com/?d=QHKY2FVW

	Here are some sketchy solutions to some extra problems. They are not complete and I still could not solve some of them.
	So of course be skeptical. -Kai http://www.2shared.com/document/eomly5cw/HW2extraproblems.html

	Also try this link http://www.megaupload.com/?d=VUUX4E8G -Kai [[User:Xwbdsb\|Xwbdsb]] 09:25, 15 October 2010 (EDT)

Drorbn: /* Suggestions for Good Deeds */

2010-10-18T17:36:20Z

Suggestions for Good Deeds

← Older revision		Revision as of 13:36, 18 October 2010
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	===Suggestions for Good Deeds===		===Suggestions for Good Deeds===
	Annotate our Monday videos (starting with {{10-327/vp\|0927}}) in a manner similar to (say) {{dbnvp link\|AKT-090910-1\|AKT-090910-1}}, and/or add links to the blackboard shots, in a manner similar to {{dbnvp link\|Alekseev-1006-1\|Alekseev-1006-1}}. Also, make ''constructive'' suggestions to me, {{Dror}} and / or the videographer, Qian (Sindy) Li, on how to improve the videos and / or the software used to display them. Note that "constructive" means also, "something that can be implemented relatively easily in the real ~~worlds~~, given limited resources".		Annotate our Monday videos (starting with {{10-327/vp\|0927}}) in a manner similar to (say) {{dbnvp link\|AKT-090910-1\|AKT-090910-1}}, and/or add links to the blackboard shots, in a manner similar to {{dbnvp link\|Alekseev-1006-1\|Alekseev-1006-1}}. Also, make ''constructive'' suggestions to me, {{Dror}} and / or the videographer, Qian (Sindy) Li, on how to improve the videos and / or the software used to display them. Note that "constructive" means also, "something that can be implemented relatively easily in the real world, given limited resources".

	{{Template:10-327:Dror/Students Divider}}		{{Template:10-327:Dror/Students Divider}}

Xwbdsb: /* Solution */

2010-10-15T13:25:03Z

Solution

← Older revision		Revision as of 09:25, 15 October 2010
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	As promised, I provide my solution to HW2 here for any one of you might care. -Kai		As promised, I provide my solution to HW2 here for any one of you might care. -Kai
	http://www.2shared.com/document/DVGaHsqO/HW2sol.html		http://www.2shared.com/document/DVGaHsqO/HW2sol.html

			Also try this link if the previous one does not work.
			http://www.megaupload.com/?d=QHKY2FVW

	Here are some sketchy solutions to some extra problems. They are not complete and I still could not solve some of them.		Here are some sketchy solutions to some extra problems. They are not complete and I still could not solve some of them.
	So of course be skeptical. -Kai http://www.2shared.com/document/eomly5cw/HW2extraproblems.html		So of course be skeptical. -Kai http://www.2shared.com/document/eomly5cw/HW2extraproblems.html

			Also try this link http://www.megaupload.com/?d=VUUX4E8G -Kai [[User:Xwbdsb\|Xwbdsb]] 09:25, 15 October 2010 (EDT)

Xwbdsb at 01:42, 15 October 2010

2010-10-15T01:42:00Z

← Older revision		Revision as of 21:42, 14 October 2010
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	As promised, I provide my solution to HW2 here for any one of you might care. -Kai		As promised, I provide my solution to HW2 here for any one of you might care. -Kai
	http://www.2shared.com/document/DVGaHsqO/HW2sol.html		http://www.2shared.com/document/DVGaHsqO/HW2sol.html

			Here are some sketchy solutions to some extra problems. They are not complete and I still could not solve some of them.
			So of course be skeptical. -Kai http://www.2shared.com/document/eomly5cw/HW2extraproblems.html

Xwbdsb: /* Solution */

2010-10-15T01:27:02Z

Solution

← Older revision		Revision as of 21:27, 14 October 2010
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	As promised, I provide my solution to HW2 here for any one of you might care. -Kai		As promised, I provide my solution to HW2 here for any one of you might care. -Kai
			http://www.2shared.com/document/DVGaHsqO/HW2sol.html

Xwbdsb: /* Questions */

2010-10-15T01:17:04Z

Questions

← Older revision		Revision as of 21:17, 14 October 2010
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	**** An arbitrary intersection of open sets is not necessarily open. This I'll say, but beyond this, it is your problem to solve. [[User:Drorbn\|Drorbn]] 16:21, 2 October 2010 (EDT)		**** An arbitrary intersection of open sets is not necessarily open. This I'll say, but beyond this, it is your problem to solve. [[User:Drorbn\|Drorbn]] 16:21, 2 October 2010 (EDT)

	Solution		===Solution===

	As promised, I provide my solution to HW2 here for any one of you might care. -Kai		As promised, I provide my solution to HW2 here for any one of you might care. -Kai

Xwbdsb at 01:16, 15 October 2010

2010-10-15T01:16:50Z

← Older revision		Revision as of 21:16, 14 October 2010
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	*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)		*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)
	**** An arbitrary intersection of open sets is not necessarily open. This I'll say, but beyond this, it is your problem to solve. [[User:Drorbn\|Drorbn]] 16:21, 2 October 2010 (EDT)		**** An arbitrary intersection of open sets is not necessarily open. This I'll say, but beyond this, it is your problem to solve. [[User:Drorbn\|Drorbn]] 16:21, 2 October 2010 (EDT)

			Solution

			As promised, I provide my solution to HW2 here for any one of you might care. -Kai

Drorbn: /* Questions */

2010-10-02T20:21:59Z

Questions

← Older revision		Revision as of 16:21, 2 October 2010
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	** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)		** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)
	*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)		*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)
			**** An arbitrary intersection of open sets is not necessarily open. This I'll say, but beyond this, it is your problem to solve. [[User:Drorbn\|Drorbn]] 16:21, 2 October 2010 (EDT)

Xwbdsb: /* Questions */

2010-10-02T15:29:55Z

Questions

← Older revision		Revision as of 11:29, 2 October 2010
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	*[[User:Xwbdsb\|Xwbdsb]] 00:39, 2 October 2010 (EDT) I have a question about problem 13 on page 101. What does <math>x\times x</math> mean when <math>x</math> is an element in <math>X</math>? Does the author mean the ordered pair <math>(x,x)</math>? And we assume that we put product topology on <math>X \times X</math>? -Kai		*[[User:Xwbdsb\|Xwbdsb]] 00:39, 2 October 2010 (EDT) I have a question about problem 13 on page 101. What does <math>x\times x</math> mean when <math>x</math> is an element in <math>X</math>? Does the author mean the ordered pair <math>(x,x)</math>? And we assume that we put product topology on <math>X \times X</math>? -Kai
	** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)		** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)
	*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open ~~nbds~~? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)		*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)

Xwbdsb: /* Questions */

2010-10-02T15:29:38Z

Questions

← Older revision		Revision as of 11:29, 2 October 2010
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	*[[User:Xwbdsb\|Xwbdsb]] 00:39, 2 October 2010 (EDT) I have a question about problem 13 on page 101. What does <math>x\times x</math> mean when <math>x</math> is an element in <math>X</math>? Does the author mean the ordered pair <math>(x,x)</math>? And we assume that we put product topology on <math>X \times X</math>? -Kai		*[[User:Xwbdsb\|Xwbdsb]] 00:39, 2 October 2010 (EDT) I have a question about problem 13 on page 101. What does <math>x\times x</math> mean when <math>x</math> is an element in <math>X</math>? Does the author mean the ordered pair <math>(x,x)</math>? And we assume that we put product topology on <math>X \times X</math>? -Kai
	** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)		** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)
	*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\~~delta~~</math> complement. So we can separate it from any point in <math>\~~delta~~</math>. But to separate it from the entire <math>\~~delta~~</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbds? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)		*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbds? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)

← Older revision		Revision as of 16:21, 2 October 2010
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	** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)		** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)
	*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)		*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)
			**** An arbitrary intersection of open sets is not necessarily open. This I'll say, but beyond this, it is your problem to solve. [[User:Drorbn\|Drorbn]] 16:21, 2 October 2010 (EDT)

← Older revision		Revision as of 11:29, 2 October 2010
Line 24:		Line 24:
	*[[User:Xwbdsb\|Xwbdsb]] 00:39, 2 October 2010 (EDT) I have a question about problem 13 on page 101. What does <math>x\times x</math> mean when <math>x</math> is an element in <math>X</math>? Does the author mean the ordered pair <math>(x,x)</math>? And we assume that we put product topology on <math>X \times X</math>? -Kai		*[[User:Xwbdsb\|Xwbdsb]] 00:39, 2 October 2010 (EDT) I have a question about problem 13 on page 101. What does <math>x\times x</math> mean when <math>x</math> is an element in <math>X</math>? Does the author mean the ordered pair <math>(x,x)</math>? And we assume that we put product topology on <math>X \times X</math>? -Kai
	** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)		** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)
	*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open ~~nbds~~? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)		*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbd? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)

← Older revision		Revision as of 11:29, 2 October 2010
Line 24:		Line 24:
	*[[User:Xwbdsb\|Xwbdsb]] 00:39, 2 October 2010 (EDT) I have a question about problem 13 on page 101. What does <math>x\times x</math> mean when <math>x</math> is an element in <math>X</math>? Does the author mean the ordered pair <math>(x,x)</math>? And we assume that we put product topology on <math>X \times X</math>? -Kai		*[[User:Xwbdsb\|Xwbdsb]] 00:39, 2 October 2010 (EDT) I have a question about problem 13 on page 101. What does <math>x\times x</math> mean when <math>x</math> is an element in <math>X</math>? Does the author mean the ordered pair <math>(x,x)</math>? And we assume that we put product topology on <math>X \times X</math>? -Kai
	** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)		** Yes and yes. [[User:Drorbn\|Drorbn]] 07:19, 2 October 2010 (EDT)
	*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\~~delta~~</math> complement. So we can separate it from any point in <math>\~~delta~~</math>. But to separate it from the entire <math>\~~delta~~</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbds? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)		*** I found a way to approach this problem but I am not sure about the technicality. <math>X \times X</math> is Hausdorff. We take any point in <math>\Delta</math> complement. So we can separate it from any point in <math>\Delta</math>. But to separate it from the entire <math>\Delta</math> we need to get the intersection of all its open nbds. Will that still be a valid open nbds? -Kai [[User:Xwbdsb\|Xwbdsb]] 11:29, 2 October 2010 (EDT)