Metrizable space
type: Ontology
creation date: 2026-03-10T00:33:00+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Metrizable space
type: Subject
type: Category:Properties of topological spaces closed under finite products
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/Metrizable_space
wiki namespace: 0
wiki page content language: en
satisfies metaproperty: Weakly hereditary property of topological spaces
satisfies metaproperty: Subspace-hereditary property of topological spaces
stronger than: Kolmogorov space
stronger than: Submetrizable space
stronger than: Ordered field-metrizable space
stronger than: Perfect space
stronger than: Regular Lindelof space
stronger than: Normal space
stronger than: Paracompact Hausdorff space
stronger than: Perfectly normal space
stronger than: Hausdorff space
stronger than: Collectionwise Hausdorff space
stronger than: Collectionwise normal space
stronger than: Elastic space
stronger than: Monotonically normal space
stronger than: Completely regular space
stronger than: First-countable space
stronger than: Hereditarily normal space
stronger than: Regular space
stronger than: T1 space
weaker than: Manifold
weaker than: Sub-Euclidean space
weaker than: Completely metrizable space
weaker than: Closed sub-Euclidean space
wiki page modification date: 2015-11-15T23:49:47Z
modification date#aux: 2457342.4929051
wiki page sort key: Metrizable 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: Metrizable space
wiki page sort key: Line with two origins

Moore plane
type: Subject
page: https://topospaces.subwiki.org/wiki/Moore_plane
wiki namespace: 0
wiki page content language: en
dissatisfies property: Metrizable 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
dissatisfies property: Metrizable 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: Metrizable 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: Metrizable 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: Metrizable space
wiki page sort key: 2-torus

Genus two surface
type: Subject
page: https://topospaces.subwiki.org/wiki/Genus_two_surface
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satisfies property: Metrizable space
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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: Metrizable space
wiki page sort key: Real projective three-dimensional space

Product of 2-sphere and circle
type: Subject
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wiki namespace: 0
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satisfies property: Metrizable space
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Product of two 2-spheres
type: Subject
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wiki namespace: 0
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satisfies property: Metrizable space
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Product of real projective plane and circle
type: Subject
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satisfies property: Metrizable space
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Product of 2-sphere and real projective plane
type: Subject
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satisfies property: Metrizable space
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Product of 3-sphere and circle
type: Subject
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satisfies property: Metrizable space
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Product of 2-sphere and 2-torus
type: Subject
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satisfies property: Metrizable space
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Pair of intersecting lines
type: Subject
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wiki namespace: 0
wiki page content language: en
satisfies property: Metrizable space
wiki page sort key: Pair of intersecting lines

Nagata-Smirnov metrization theorem
type: Subject
page: https://topospaces.subwiki.org/wiki/Nagata-2DSmirnov_metrization_theorem
wiki namespace: 0
wiki page content language: en
proves property satisfactin of: Metrizable space
wiki page sort key: Nagata-Smirnov metrization theorem

Smirnov metrization theorem
type: Subject
page: https://topospaces.subwiki.org/wiki/Smirnov_metrization_theorem
wiki namespace: 0
wiki page content language: en
proves property satisfactin of: Metrizable space
wiki page sort key: Smirnov metrization theorem

Urysohn metrization theorem
type: Subject
page: https://topospaces.subwiki.org/wiki/Urysohn_metrization_theorem
wiki namespace: 0
wiki page content language: en
proves property satisfactin of: Metrizable space
wiki page sort key: Urysohn metrization theorem

Collectionwise normal and Moore implies metrizable
type: Subject
page: https://topospaces.subwiki.org/wiki/Collectionwise_normal_and_Moore_implies_metrizable
wiki namespace: 0
wiki page content language: en
proves property satisfactin of: Metrizable space
wiki page sort key: Collectionwise normal and Moore implies metrizable
proves property satisfaction of: Metrizable space

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

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

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

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

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

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

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

Protometrizable space
type: Subject
page: https://topospaces.subwiki.org/wiki/Protometrizable_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Protometrizable space

Normal space
type: Subject
page: https://topospaces.subwiki.org/wiki/Normal_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Normal space

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

Perfectly normal space
type: Subject
page: https://topospaces.subwiki.org/wiki/Perfectly_normal_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Perfectly normal space

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

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

Collectionwise normal space
type: Subject
page: https://topospaces.subwiki.org/wiki/Collectionwise_normal_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Collectionwise normal space

Elastic space
type: Subject
page: https://topospaces.subwiki.org/wiki/Elastic_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Elastic space

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

Hereditarily collectionwise normal space
type: Subject
page: https://topospaces.subwiki.org/wiki/Hereditarily_collectionwise_normal_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Hereditarily collectionwise normal space

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

Paracompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Paracompact_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Paracompact space

Compactly generated space
type: Subject
page: https://topospaces.subwiki.org/wiki/Compactly_generated_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Compactly generated space

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

Hereditarily normal space
type: Subject
page: https://topospaces.subwiki.org/wiki/Hereditarily_normal_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Hereditarily normal space

Regular space
type: Subject
page: https://topospaces.subwiki.org/wiki/Regular_space
wiki namespace: 0
wiki page content language: en
weaker than: Metrizable space
wiki page sort key: Regular space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Nagata-2DSmirnov_metrization_theorem-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Nagata-Smirnov metrization theorem
wiki namespace: 0
wiki page sort key: Nagata-Smirnov metrization theorem#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Smirnov_metrization_theorem-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Smirnov metrization theorem
wiki namespace: 0
wiki page sort key: Smirnov metrization theorem#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Urysohn_metrization_theorem-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Urysohn metrization theorem
wiki namespace: 0
wiki page sort key: Urysohn metrization theorem#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Metrizable_implies_perfectly_normal-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Metrizable implies perfectly normal
wiki namespace: 0
wiki page sort key: Metrizable implies perfectly normal#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Metrizability_is_hereditary-23_6824aae1e8c269fe8d977bb5ddf5a0f2
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Metrizability_is_hereditary
wiki namespace: 0
wiki page sort key: Metrizability is hereditary#Metrizable space;1# 6824aae1e8c269fe8d977bb5ddf5a0f2
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Metrizable_implies_hereditarily_normal-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Metrizable implies hereditarily normal
wiki namespace: 0
wiki page sort key: Metrizable implies hereditarily normal#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Metrizable_implies_compactly_generated-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Metrizable implies compactly generated
wiki namespace: 0
wiki page sort key: Metrizable implies compactly generated#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Metrizable_implies_first-2Dcountable-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Metrizable implies first-countable
wiki namespace: 0
wiki page sort key: Metrizable implies first-countable#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Collectionwise_normal_and_Moore_implies_metrizable-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Collectionwise normal and Moore implies metrizable
wiki namespace: 0
wiki page sort key: Collectionwise normal and Moore implies metrizable#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Metrizable_implies_monotonically_normal-23_83f8e8c9175845e1544f74148758b182
type: Subject
master page: Metrizable implies monotonically normal
wiki namespace: 0
wiki page sort key: Metrizable implies monotonically normal#Metrizable space;2# 83f8e8c9175845e1544f74148758b182
page: Metrizable space

Metrizable implies monotonically normal
type: Subject
page: https://topospaces.subwiki.org/wiki/Metrizable_implies_monotonically_normal
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Metrizable space
wiki page sort key: Metrizable implies monotonically normal

Metrizable implies perfectly normal
type: Subject
page: https://topospaces.subwiki.org/wiki/Metrizable_implies_perfectly_normal
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Metrizable space
wiki page sort key: Metrizable implies perfectly normal

Metrizable implies hereditarily normal
type: Subject
page: https://topospaces.subwiki.org/wiki/Metrizable_implies_hereditarily_normal
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Metrizable space
wiki page sort key: Metrizable implies hereditarily normal

Metrizable implies compactly generated
type: Subject
page: https://topospaces.subwiki.org/wiki/Metrizable_implies_compactly_generated
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Metrizable space
wiki page sort key: Metrizable implies compactly generated

Metrizable implies first-countable
type: Subject
page: https://topospaces.subwiki.org/wiki/Metrizable_implies_first-2Dcountable
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Metrizable space
wiki page sort key: Metrizable implies first-countable

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

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

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

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

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

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