Compact space
type: Ontology
creation date: 2026-02-04T00:30:46+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Compact space
type: Subject
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/Compact_space
wiki namespace: 0
wiki page content language: en
dissatisfies metaproperty: Subspace-hereditary property of topological spaces
satisfies metaproperty: Product-closed property of topological spaces
satisfies metaproperty: Weakly hereditary property of topological spaces
satisfies metaproperty: Fiber-bundle-closed property of topological spaces
satisfies metaproperty: Continuous image-closed property of topological spaces
satisfies metaproperty: Coarsening-preserved property of topological spaces
stronger than: Locally compact space
stronger than: Paracompact space
stronger than: Limit point-compact space
stronger than: Countably compact space
stronger than: Sequentially compact space
stronger than: Lindelof space
weaker than: Compact Hausdorff space
weaker than: Compact metrizable space
weaker than: Compact polyhedron
weaker than: Compact manifold
weaker than: Supercompact space
weaker than: Noetherian space
weaker than: Hereditarily compact space
weaker than: Finite space
wiki page modification date: 2015-11-16T01:56:46Z
modification date#aux: 2457342.581088
wiki page sort key: Compact space

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type: Subject
master page: Compact space
wiki namespace: 0
wiki page sort key: Compact space#Munkres
page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Book-3AMunkres

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type: Subject
master page: Compact space
wiki namespace: 0
wiki page sort key: Compact space#SingerThorpe
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type: Subject
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type: Subject
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type: Subject
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wiki page sort key: Compact space# QUERYa491636999c0f04f7baebd4b9d843522

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: Compact 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: Compact space
wiki page sort key: Moore plane

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

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

Product of real projective plane and circle
type: Subject
page: https://topospaces.subwiki.org/wiki/Product_of_real_projective_plane_and_circle
wiki namespace: 0
wiki page content language: en
satisfies property: Compact space
wiki page sort key: Product of real projective plane and circle

Product of 2-sphere and real projective plane
type: Subject
page: https://topospaces.subwiki.org/wiki/Product_of_2-2Dsphere_and_real_projective_plane
wiki namespace: 0
wiki page content language: en
satisfies property: Compact space
wiki page sort key: Product of 2-sphere and real projective plane

Product of 3-sphere and circle
type: Subject
page: https://topospaces.subwiki.org/wiki/Product_of_3-2Dsphere_and_circle
wiki namespace: 0
wiki page content language: en
satisfies property: Compact space
wiki page sort key: Product of 3-sphere and circle

Product of 2-sphere and 2-torus
type: Subject
page: https://topospaces.subwiki.org/wiki/Product_of_2-2Dsphere_and_2-2Dtorus
wiki namespace: 0
wiki page content language: en
satisfies property: Compact space
wiki page sort key: Product of 2-sphere and 2-torus

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
satisfies property: Compact 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
satisfies property: Compact space
wiki page sort key: Sierpiński space

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

Compact T1 space
type: Subject
page: https://topospaces.subwiki.org/wiki/Compact_T1_space
wiki namespace: 0
wiki page content language: en
stronger than: Compact space
wiki page sort key: Compact T1 space

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

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

Feebly compact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Feebly_compact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Feebly compact space
weaker than: Compact space

Pseudocompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Pseudocompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Pseudocompact space
weaker than: Compact space

H-closed space
type: Subject
page: https://topospaces.subwiki.org/wiki/H-2Dclosed_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: H-closed space

Hemicompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Hemicompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Hemicompact space

Hurewicz space
type: Subject
page: https://topospaces.subwiki.org/wiki/Hurewicz_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Hurewicz space

Metacompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Metacompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Metacompact space
weaker than: Compact space

Orthocompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Orthocompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Orthocompact space

Nearly metacompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Nearly_metacompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Nearly metacompact space

N-pseudocompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/N-2Dpseudocompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: N-pseudocompact space

Strongly paracompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Strongly_paracompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Strongly paracompact space

Product-transitively paracompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Product-2Dtransitively_paracompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Product-transitively paracompact space

Realcompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Realcompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Realcompact space

Sigma-compact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Sigma-2Dcompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Sigma-compact space

Snake-like space
type: Subject
page: https://topospaces.subwiki.org/wiki/Snake-2Dlike_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Snake-like space

Strongly locally compact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Strongly_locally_compact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Strongly locally compact space

Subparacompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Subparacompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Subparacompact space

Ultraparacompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Ultraparacompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Ultraparacompact space

Supercompact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Supercompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Supercompact space

Locally compact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Locally_compact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Locally compact space

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

Limit point-compact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Limit_point-2Dcompact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Limit point-compact space

Countably compact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Countably_compact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Countably compact space

Sequentially compact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Sequentially_compact_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Sequentially compact space

Lindelof space
type: Subject
page: https://topospaces.subwiki.org/wiki/Lindelof_space
wiki namespace: 0
wiki page content language: en
variation of: Compact space
wiki page sort key: Lindelof space

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

Rim-compact space
type: Subject
page: https://topospaces.subwiki.org/wiki/Rim-2Dcompact_space
wiki namespace: 0
wiki page content language: en
weaker than: Compact space
wiki page sort key: Rim-compact space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Hausdorff_implies_KC-23_c086023d7abc7490360c9641b5d779e6
type: Subject
master page: Hausdorff implies KC
wiki namespace: 0
wiki page sort key: Hausdorff implies KC#Compact space;2# c086023d7abc7490360c9641b5d779e6
page: Compact space

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type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Tube_lemma
wiki namespace: 0
wiki page sort key: Tube lemma#Compact space;1# 152b8968f88dfc9d64d515f01a21d4de
page: Compact space

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type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Compact_times_metacompact_implies_metacompact
wiki namespace: 0
wiki page sort key: Compact times metacompact implies metacompact#Compact space# d5d0ae527b481960e5a0e9edc4bcfcfc
page: Compact space

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type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Compactness_is_continuous_image-2Dclosed
wiki namespace: 0
wiki page sort key: Compactness is continuous image-closed#Compact space;1# 152b8968f88dfc9d64d515f01a21d4de
page: Compact space

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type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Compactness_is_coarsening-2Dpreserved
wiki namespace: 0
wiki page sort key: Compactness is coarsening-preserved#Compact space;1# 152b8968f88dfc9d64d515f01a21d4de
page: Compact space

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type: Subject
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Proving compactness
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Compactness
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Dissatisfies property
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Satisfies property
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Defining ingredient
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Stronger than
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Variation of
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Weaker than
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Page
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Survey article about
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REDI
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