Hausdorff space
type: Ontology
creation date: 2025-11-13T06:42:37+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Hausdorff space
type: Subject
type: Category:Properties of topological spaces in the T family
type: Category:Separation-related properties of topological spaces
type: Category:Properties of topological spaces
type: Category:Basic definitions in topology
type: Category:Standard terminology
type: Category:Pivotal properties of topological spaces
page: https://topospaces.subwiki.org/wiki/Hausdorff_space
wiki namespace: 0
wiki page content language: en
defining ingredient: Product topology
defining ingredient: Closed subset
dissatisfies metaproperty: Local property of topological spaces
satisfies metaproperty: Box product-closed property of topological spaces
satisfies metaproperty: Refining-preserved property of topological spaces
satisfies metaproperty: Closure-local property of topological spaces
satisfies metaproperty: Product-closed property of topological spaces
satisfies metaproperty: Subspace-hereditary property of topological spaces
stronger than: KC-space
stronger than: Preregular space
stronger than: Locally Hausdorff space
stronger than: Weakly Hausdorff space
stronger than: US-space
stronger than: Sober space
stronger than: Sober T1 space
stronger than: Kolmogorov space
stronger than: Sober T0 space
stronger than: T1 space
weaker than: Manifold
weaker than: Normal Hausdorff space
weaker than: Collectionwise normal Hausdorff space
weaker than: Regular Hausdorff space
weaker than: Tychonoff space
weaker than: Submetrizable space
weaker than: CW-space
weaker than: Collectionwise Hausdorff space
weaker than: Metrizable space
weaker than: Functionally Hausdorff space
weaker than: Urysohn space
wiki page modification date: 2017-01-05T01:36:31Z
modification date#aux: 2457758.5670255
wiki page sort key: Hausdorff space

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query string: Hausdorff space Manifold
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query string: Hausdorff space Submetrizable space
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Line with two origins
type: Subject
page: https://topospaces.subwiki.org/wiki/Line_with_two_origins
wiki namespace: 0
wiki page content language: en
dissatisfies property: Hausdorff space
wiki page sort key: Line with two origins

Countable space with cofinite topology
type: Subject
page: https://topospaces.subwiki.org/wiki/Countable_space_with_cofinite_topology
wiki namespace: 0
wiki page content language: en
dissatisfies property: Hausdorff space
wiki page sort key: Countable space with cofinite topology

Sierpiński space
type: Subject
page: https://topospaces.subwiki.org/wiki/Sierpiński_space
wiki namespace: 0
wiki page content language: en
dissatisfies property: Hausdorff space
wiki page sort key: Sierpiński space

Moore plane
type: Subject
page: https://topospaces.subwiki.org/wiki/Moore_plane
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Moore plane

Sorgenfrey line
type: Subject
page: https://topospaces.subwiki.org/wiki/Sorgenfrey_line
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Sorgenfrey line

2-sphere
type: Subject
page: https://topospaces.subwiki.org/wiki/2-2Dsphere
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: 2-sphere

Real projective plane
type: Subject
page: https://topospaces.subwiki.org/wiki/Real_projective_plane
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Real projective plane

2-torus
type: Subject
page: https://topospaces.subwiki.org/wiki/2-2Dtorus
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: 2-torus

Genus two surface
type: Subject
page: https://topospaces.subwiki.org/wiki/Genus_two_surface
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Genus two surface

Real projective three-dimensional space
type: Subject
page: https://topospaces.subwiki.org/wiki/Real_projective_three-2Ddimensional_space
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Real projective three-dimensional space

Product of 2-sphere and circle
type: Subject
page: https://topospaces.subwiki.org/wiki/Product_of_2-2Dsphere_and_circle
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Product of 2-sphere and circle

Product of two 2-spheres
type: Subject
page: https://topospaces.subwiki.org/wiki/Product_of_two_2-2Dspheres
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Product of two 2-spheres

Product of real projective plane and circle
type: Subject
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wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Product of real projective plane and circle

Product of 2-sphere and real projective plane
type: Subject
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satisfies property: Hausdorff space
wiki page sort key: Product of 2-sphere and real projective plane

Product of 3-sphere and circle
type: Subject
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wiki namespace: 0
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satisfies property: Hausdorff space
wiki page sort key: Product of 3-sphere and circle

Product of 2-sphere and 2-torus
type: Subject
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wiki namespace: 0
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satisfies property: Hausdorff space
wiki page sort key: Product of 2-sphere and 2-torus

Pair of intersecting lines
type: Subject
page: https://topospaces.subwiki.org/wiki/Pair_of_intersecting_lines
wiki namespace: 0
wiki page content language: en
satisfies property: Hausdorff space
wiki page sort key: Pair of intersecting lines

Manifold
type: Subject
page: https://topospaces.subwiki.org/wiki/Manifold
wiki namespace: 0
wiki page content language: en
defining ingredient: Hausdorff space
wiki page sort key: Manifold
stronger than: Hausdorff space

Manifold with boundary
type: Subject
page: https://topospaces.subwiki.org/wiki/Manifold_with_boundary
wiki namespace: 0
wiki page content language: en
defining ingredient: Hausdorff space
wiki page sort key: Manifold with boundary

Preregular space
type: Subject
page: https://topospaces.subwiki.org/wiki/Preregular_space
wiki namespace: 0
wiki page content language: en
defining ingredient: Hausdorff space
wiki page sort key: Preregular space
weaker than: Hausdorff space

Regular Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Regular_Hausdorff_space
wiki namespace: 0
wiki page content language: en
defining ingredient: Hausdorff space
wiki page sort key: Regular Hausdorff space
stronger than: Hausdorff space

Hereditarily normal Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Hereditarily_normal_Hausdorff_space
wiki namespace: 0
wiki page content language: en
defining ingredient: Hausdorff space
wiki page sort key: Hereditarily normal Hausdorff space

Compactly generated Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Compactly_generated_Hausdorff_space
wiki namespace: 0
wiki page content language: en
defining ingredient: Hausdorff space
wiki page sort key: Compactly generated Hausdorff space

Connected manifold
type: Subject
page: https://topospaces.subwiki.org/wiki/Connected_manifold
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Connected manifold

Normal Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Normal_Hausdorff_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Normal Hausdorff space

Tychonoff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Tychonoff_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Tychonoff space

Submetrizable space
type: Subject
page: https://topospaces.subwiki.org/wiki/Submetrizable_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Submetrizable space

Moore space
type: Subject
page: https://topospaces.subwiki.org/wiki/Moore_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Moore space

One-point space
type: Subject
page: https://topospaces.subwiki.org/wiki/One-2Dpoint_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: One-point space

CW-space
type: Subject
page: https://topospaces.subwiki.org/wiki/CW-2Dspace
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: CW-space

Collectionwise Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Collectionwise_Hausdorff_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Collectionwise Hausdorff space
variation of: Hausdorff space

Metrizable space
type: Subject
page: https://topospaces.subwiki.org/wiki/Metrizable_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Metrizable space

Linearly orderable space
type: Subject
page: https://topospaces.subwiki.org/wiki/Linearly_orderable_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Linearly orderable space

Monotonically normal space
type: Subject
page: https://topospaces.subwiki.org/wiki/Monotonically_normal_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Monotonically normal space

Completely regular space
type: Subject
page: https://topospaces.subwiki.org/wiki/Completely_regular_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Completely regular space

Functionally Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Functionally_Hausdorff_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Functionally Hausdorff space
variation of: Hausdorff space

Urysohn space
type: Subject
page: https://topospaces.subwiki.org/wiki/Urysohn_space
wiki namespace: 0
wiki page content language: en
stronger than: Hausdorff space
wiki page sort key: Urysohn space

Connected Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Connected_Hausdorff_space
wiki namespace: 0
wiki page content language: en
variation of: Hausdorff space
wiki page sort key: Connected Hausdorff space

KC-space
type: Subject
page: https://topospaces.subwiki.org/wiki/KC-2Dspace
wiki namespace: 0
wiki page content language: en
variation of: Hausdorff space
wiki page sort key: KC-space
weaker than: Hausdorff space

Locally Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Locally_Hausdorff_space
wiki namespace: 0
wiki page content language: en
variation of: Hausdorff space
wiki page sort key: Locally Hausdorff space
weaker than: Hausdorff space

US-space
type: Subject
page: https://topospaces.subwiki.org/wiki/US-2Dspace
wiki namespace: 0
wiki page content language: en
variation of: Hausdorff space
wiki page sort key: US-space

Weakly Hausdorff space
type: Subject
page: https://topospaces.subwiki.org/wiki/Weakly_Hausdorff_space
wiki namespace: 0
wiki page content language: en
weaker than: Hausdorff space
wiki page sort key: Weakly Hausdorff space

Sober space
type: Subject
page: https://topospaces.subwiki.org/wiki/Sober_space
wiki namespace: 0
wiki page content language: en
weaker than: Hausdorff space
wiki page sort key: Sober space

Sober T1 space
type: Subject
page: https://topospaces.subwiki.org/wiki/Sober_T1_space
wiki namespace: 0
wiki page content language: en
weaker than: Hausdorff space
wiki page sort key: Sober T1 space

Kolmogorov space
type: Subject
page: https://topospaces.subwiki.org/wiki/Kolmogorov_space
wiki namespace: 0
wiki page content language: en
weaker than: Hausdorff space
wiki page sort key: Kolmogorov space

Sober T0 space
type: Subject
page: https://topospaces.subwiki.org/wiki/Sober_T0_space
wiki namespace: 0
wiki page content language: en
weaker than: Hausdorff space
wiki page sort key: Sober T0 space

Symmetric space
type: Subject
page: https://topospaces.subwiki.org/wiki/Symmetric_space
wiki namespace: 0
wiki page content language: en
weaker than: Hausdorff space
wiki page sort key: Symmetric space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorff_implies_KC-23_351e99434404b13c331ee1e810406557
type: Subject
master page: Hausdorff implies KC
wiki namespace: 0
wiki page sort key: Hausdorff implies KC#Hausdorff space;2# 351e99434404b13c331ee1e810406557
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorffness_is_hereditary-23_735e04ba2bb4d11dd9bed692cfdd529c
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorffness_is_hereditary
wiki namespace: 0
wiki page sort key: Hausdorffness is hereditary#Hausdorff space;1# 735e04ba2bb4d11dd9bed692cfdd529c
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorffness_is_product-2Dclosed-23_735e04ba2bb4d11dd9bed692cfdd529c
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorffness_is_product-2Dclosed
wiki namespace: 0
wiki page sort key: Hausdorffness is product-closed#Hausdorff space;1# 735e04ba2bb4d11dd9bed692cfdd529c
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Locally_Hausdorff_not_implies_Hausdorff-23_d4c8d879c9e72cccb5b13697d46de567
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Locally_Hausdorff_not_implies_Hausdorff
wiki namespace: 0
wiki page sort key: Locally Hausdorff not implies Hausdorff#Hausdorff space# d4c8d879c9e72cccb5b13697d46de567
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorffness_is_refining-2Dpreserved-23_735e04ba2bb4d11dd9bed692cfdd529c
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorffness_is_refining-2Dpreserved
wiki namespace: 0
wiki page sort key: Hausdorffness is refining-preserved#Hausdorff space;1# 735e04ba2bb4d11dd9bed692cfdd529c
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Paracompact_Hausdorff_implies_normal-23_d4c8d879c9e72cccb5b13697d46de567
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Paracompact_Hausdorff_implies_normal
wiki namespace: 0
wiki page sort key: Paracompact Hausdorff implies normal#Hausdorff space# d4c8d879c9e72cccb5b13697d46de567
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Paracompact_Hausdorff_implies_binormal-23_d4c8d879c9e72cccb5b13697d46de567
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Paracompact_Hausdorff_implies_binormal
wiki namespace: 0
wiki page sort key: Paracompact Hausdorff implies binormal#Hausdorff space# d4c8d879c9e72cccb5b13697d46de567
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorff_implies_sober-23_351e99434404b13c331ee1e810406557
type: Subject
master page: Hausdorff implies sober
wiki namespace: 0
wiki page sort key: Hausdorff implies sober#Hausdorff space;2# 351e99434404b13c331ee1e810406557
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorff_implies_T1-23_351e99434404b13c331ee1e810406557
type: Subject
master page: Hausdorff implies T1
wiki namespace: 0
wiki page sort key: Hausdorff implies T1#Hausdorff space;2# 351e99434404b13c331ee1e810406557
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/T1_not_implies_Hausdorff-23_d4c8d879c9e72cccb5b13697d46de567
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/T1_not_implies_Hausdorff
wiki namespace: 0
wiki page sort key: T1 not implies Hausdorff#Hausdorff space# d4c8d879c9e72cccb5b13697d46de567
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/US_not_implies_Hausdorff-23_d4c8d879c9e72cccb5b13697d46de567
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/US_not_implies_Hausdorff
wiki namespace: 0
wiki page sort key: US not implies Hausdorff#Hausdorff space# d4c8d879c9e72cccb5b13697d46de567
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorff_implies_US-23_351e99434404b13c331ee1e810406557
type: Subject
master page: Hausdorff implies US
wiki namespace: 0
wiki page sort key: Hausdorff implies US#Hausdorff space;2# 351e99434404b13c331ee1e810406557
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Suspension_of_Hausdorff_space_is_Hausdorff-23_d4c8d879c9e72cccb5b13697d46de567
type: Subject
master page: Suspension of Hausdorff space is Hausdorff
wiki namespace: 0
wiki page sort key: Suspension of Hausdorff space is Hausdorff#Hausdorff space# d4c8d879c9e72cccb5b13697d46de567
page: Hausdorff space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorffness_is_closure-2Dlocal-23_735e04ba2bb4d11dd9bed692cfdd529c
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorffness_is_closure-2Dlocal
wiki namespace: 0
wiki page sort key: Hausdorffness is closure-local#Hausdorff space;1# 735e04ba2bb4d11dd9bed692cfdd529c
page: Hausdorff space

Suspension of Hausdorff space is Hausdorff
type: Subject
page: https://topospaces.subwiki.org/wiki/Suspension_of_Hausdorff_space_is_Hausdorff
wiki namespace: 0
wiki page content language: en
proves property satisfaction of: Hausdorff space
wiki page sort key: Suspension of Hausdorff space is Hausdorff
uses property satisfaction of: Hausdorff space

Hausdorff implies sober
type: Subject
page: https://topospaces.subwiki.org/wiki/Hausdorff_implies_sober
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Hausdorff space
wiki page sort key: Hausdorff implies sober

Hausdorff implies T1
type: Subject
page: https://topospaces.subwiki.org/wiki/Hausdorff_implies_T1
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Hausdorff space
wiki page sort key: Hausdorff implies T1

Hausdorff implies US
type: Subject
page: https://topospaces.subwiki.org/wiki/Hausdorff_implies_US
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Hausdorff space
wiki page sort key: Hausdorff implies US

Irreducible and Hausdorff implies one-point space
type: Subject
page: https://topospaces.subwiki.org/wiki/Irreducible_and_Hausdorff_implies_one-2Dpoint_space
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Hausdorff space
wiki page sort key: Irreducible and Hausdorff implies one-point space

Hausdorff implies KC
type: Subject
page: https://topospaces.subwiki.org/wiki/Hausdorff_implies_KC
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Hausdorff space
wiki page sort key: Hausdorff implies KC

Importance of Hausdorffness
type: Subject
page: https://topospaces.subwiki.org/wiki/Importance_of_Hausdorffness
wiki namespace: 0
wiki page content language: en
survey article about: Hausdorff space
wiki page sort key: Importance of Hausdorffness

Varying Hausdorffness
type: Subject
page: https://topospaces.subwiki.org/wiki/Varying_Hausdorffness
wiki namespace: 0
wiki page content language: en
survey article about: Hausdorff space
wiki page sort key: Varying Hausdorffness

Hausdorffness
type: Subject
page: https://topospaces.subwiki.org/wiki/Hausdorffness
wiki namespace: 0
wiki page content language: en
redirects to: Hausdorff space
wiki page sort key: Hausdorffness

Dissatisfies property
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3ADissatisfies_property
wiki namespace: 132
wiki page content language: en
wiki page sort key: Dissatisfies property

Satisfies property
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3ASatisfies_property
wiki namespace: 132
wiki page content language: en
wiki page sort key: Satisfies property

Defining ingredient
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3ADefining_ingredient
wiki namespace: 132
wiki page content language: en
wiki page sort key: Defining ingredient

Stronger than
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3AStronger_than
wiki namespace: 132
wiki page content language: en
wiki page sort key: Stronger than

Variation of
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3AVariation_of
wiki namespace: 132
wiki page content language: en
wiki page sort key: Variation of

Weaker than
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3AWeaker_than
wiki namespace: 132
wiki page content language: en
wiki page sort key: Weaker than

Page
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3APage
wiki namespace: 132
wiki page content language: en
wiki page sort key: Page

Proves property satisfaction of
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3AProves_property_satisfaction_of
wiki namespace: 132
wiki page content language: en
wiki page sort key: Proves property satisfaction of

Uses property satisfaction of
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3AUses_property_satisfaction_of
wiki namespace: 132
wiki page content language: en
wiki page sort key: Uses property satisfaction of

Survey article about
type: ObjectProperty
page: https://topospaces.subwiki.org/wiki/Property-3ASurvey_article_about
wiki namespace: 132
wiki page content language: en
wiki page sort key: Survey article about

REDI
type: DatatypeProperty
page: https://topospaces.subwiki.org/wiki/Property-3A_REDI
wiki namespace: 132
wiki page content language: en
wiki page sort key: REDI