Preregular space - Revision history

Vipul: /* Relation with other properties */

2012-01-28T15:36:51Z

Relation with other properties

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 | [[Weaker than::regular space]] || || || || {{intermediate notions short|preregular space|regular space}}
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Vipul at 02:17, 28 January 2012

2012-01-28T02:17:47Z

← Older revision		Revision as of 02:17, 28 January 2012
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	==Definition==		==Definition==

	A [[topological space]] is termed '''preregular''' if ~~any~~ two [[topologically distinguishable points]] can be separated by pairwise disjoint [[open subset]]s.		A [[topological space]] is termed '''preregular''' if it satisfies the following equivalent conditions:

			# Any two [[defining ingredient::topological indistinguishability\|topologically distinguishable points]] can be separated by pairwise disjoint [[open subset]]s.
			# Its [[defining ingredient::Kolmogorov quotient]] is a [[defining ingredient::Hausdorff space]].

	{{topospace property}}		{{topospace property}}

Vipul: Created page with "==Definition== A topological space is termed '''preregular''' if any two topologically distinguishable points can be separated by pairwise disjoint open subsets. ..."

2012-01-28T02:03:23Z

Created page with "==Definition== A topological space is termed '''preregular''' if any two topologically distinguishable points can be separated by pairwise disjoint open subsets. ..."

New page

==Definition==

A [[topological space]] is termed '''preregular''' if any two [[topologically distinguishable points]] can be separated by pairwise disjoint [[open subset]]s.

{{topospace property}}

==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]] || || || || {{intermediate notions short|preregular space|Hausdorff space}}
|-
| [[Weaker than::regular space]] || || || || {{intermediate notions short|preregular space|regular space}}
|}