Locally Hausdorff not implies Hausdorff - Revision history

Vipul: /* Related facts */

2012-01-28T00:00:08Z

Related facts

← Older revision		Revision as of 00:00, 28 January 2012
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	* [[Hausdorffness is closure-local]]		* [[Hausdorffness is closure-local]]
	* [[Hausdorffness is ~~not~~ hereditary]]		* [[Hausdorffness is hereditary]]

	==Proof==		==Proof==

	An example is the [[line with two origins]], which illustrates the more general fact that a [[locally Euclidean space]] need not be Hausdorff, and hence need not be a manifold.		An example is the [[line with two origins]], which illustrates the more general fact that a [[locally Euclidean space]] need not be Hausdorff, and hence need not be a manifold.

Vipul at 23:59, 27 January 2012

2012-01-27T23:59:52Z

← Older revision		Revision as of 23:59, 27 January 2012
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	{{topospace property non-implication}}		{{topospace property non-implication\|
			stronger = locally Hausdorff space\|
			weaker = Hausdorff space}}
	==Statement==		==Statement==

	A [[locally Hausdorff space]] need not be [[Hausdorff space\|Hausdorff]].		A [[locally Hausdorff space]] need not be [[Hausdorff space\|Hausdorff]].

	==~~Example~~==		==Related facts==

			* [[Hausdorffness is closure-local]]
			* [[Hausdorffness is not hereditary]]

			==Proof==

	An example is the [[line with two origins]], which illustrates the more general fact that a [[locally Euclidean space]] need not be Hausdorff, and hence need not be a manifold.		An example is the [[line with two origins]], which illustrates the more general fact that a [[locally Euclidean space]] need not be Hausdorff, and hence need not be a manifold.

Vipul: 2 revisions

2008-05-11T19:48:44Z

2 revisions

← Older revision	Revision as of 19:48, 11 May 2008
(No difference)

Vipul at 22:47, 15 December 2007

2007-12-15T22:47:03Z

← Older revision		Revision as of 22:47, 15 December 2007
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			{{topospace property non-implication}}
	==Statement==		==Statement==

Vipul at 22:46, 15 December 2007

2007-12-15T22:46:32Z

New page

==Statement==

A [[locally Hausdorff space]] need not be [[Hausdorff space|Hausdorff]].

==Example==

An example is the [[line with two origins]], which illustrates the more general fact that a [[locally Euclidean space]] need not be Hausdorff, and hence need not be a manifold.