Vipul: /* Relation with other properties */

2013-07-17T23:25:15Z

Relation with other properties

← Older revision		Revision as of 23:25, 17 July 2013
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	\| [[Weaker than::Hausdorff space]] \|\| any two distinct points are separated by disjoint open subsets \|\| \|\| \|\| {{intermediate notions short\|weakly Hausdorff space\|Hausdorff space}}		\| [[Weaker than::Hausdorff space]] \|\| any two distinct points are separated by disjoint open subsets \|\| \|\| \|\| {{intermediate notions short\|weakly Hausdorff space\|Hausdorff space}}
			\|-
			\| [[Stronger than::KC-space]] \|\| every compact subset of the space is closed \|\| \|\| \|\| {{intermediate notions short\|KC-space\|weakly Hausdorff space}}
	\|}		\|}

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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions		! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
	\|-
	~~\| [[Stronger than::KC-space]] \|\| every compact subset of the space is closed \|\| \|\| \|\| {{intermediate notions short\|KC-space\|weakly Hausdorff space}}~~
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	\| [[Stronger than::US-space]] \|\| every sequence of points in the space has at most one limit \|\| \|\| \|\| {{intermediate notions short\|US-space\|weakly Hausdorff space}}		\| [[Stronger than::US-space]] \|\| every sequence of points in the space has at most one limit \|\| \|\| \|\| {{intermediate notions short\|US-space\|weakly Hausdorff space}}

Vipul: Created page with "{{topospace property}} ==Definition== A topological space $X$ is termed a '''weak Hausdorff space'''' or '''weakly Hausdorff space''' if for every compact H..."

2013-07-17T23:19:09Z

Created page with "{{topospace property}} ==Definition== A topological space <math>X</math> is termed a '''weak Hausdorff space'''' or '''weakly Hausdorff space''' if for every compact H..."

New page

{{topospace property}}

==Definition==

A [[topological space]] <math>X</math> is termed a '''weak Hausdorff space'''' or '''weakly Hausdorff space''' if for every [[compact Hausdorff space]] <math>K</math> and every [[continouus map]] <math>f:K \to X</math>, the image <math>f(K)</math> is a [[closed subset]] of <math>X</math>.

==Relation with other properties==

===Stronger properties===

{| class="sortable" border="1"
! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
|-
| [[Weaker than::Hausdorff space]] || any two distinct points are separated by disjoint open subsets || || || {{intermediate notions short|weakly Hausdorff space|Hausdorff space}}
|}

===Weaker properties===

{| class="sortable" border="1"
! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
|-
| [[Stronger than::KC-space]] || every compact subset of the space is closed || || || {{intermediate notions short|KC-space|weakly Hausdorff space}}
|-
| [[Stronger than::US-space]] || every sequence of points in the space has at most one limit || || || {{intermediate notions short|US-space|weakly Hausdorff space}}
|-
| [[Stronger than::T1 space]] || every singleton subset is closed || || || {{intermediate notions short|T1 space|weakly Hausdorff space}}
|}

Weakly Hausdorff space - Revision history

Vipul: /* Relation with other properties */

Vipul: Created page with "{{topospace property}} ==Definition== A topological space X is termed a '''weak Hausdorff space'''' or '''weakly Hausdorff space''' if for every compact H..."

Vipul: Created page with "{{topospace property}} ==Definition== A topological space $X$ is termed a '''weak Hausdorff space'''' or '''weakly Hausdorff space''' if for every compact H..."