Connected space
type: Ontology
creation date: 2026-07-19T00:23:20+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Connected space
type: Subject
type: Category:Properties of topological spaces
type: Category:Homotopy-invariant 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/Connected_space
wiki namespace: 0
wiki page content language: en
defining ingredient: Open subset
defining ingredient: Closed subset
dissatisfies metaproperty: Box product-closed property of topological spaces
dissatisfies metaproperty: Weakly hereditary property of topological spaces
dissatisfies metaproperty: Subspace-hereditary property of topological spaces
satisfies metaproperty: Connected union-closed property of topological spaces
satisfies metaproperty: Closure-preserved property of topological spaces
satisfies metaproperty: Product-closed property of topological spaces
satisfies metaproperty: Continuous image-closed property of topological spaces
satisfies metaproperty: Coarsening-preserved property of topological spaces
stronger than: Space with finitely many connected components
stronger than: Space with finitely many quasicomponents
stronger than: Space in which all connected components are open
stronger than: Space in which the connected components coincide with the quasicomponents
weaker than: Path-connected space
weaker than: Simply connected space
weaker than: Irreducible space
weaker than: Ultraconnected space
weaker than: Contractible space
wiki page modification date: 2017-01-05T00:36:52Z
modification date#aux: 2457758.5256019
wiki page sort key: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_1361304f7f8c4bc1141ce6f55572c0eb
type: Subject
master page: Connected space
wiki namespace: 0
wiki page sort key: Connected space#Munkres
page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Book-3AMunkres

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_857e7c5cc8e9160e95d5c7895b88fd66
type: Subject
master page: Connected space
wiki namespace: 0
wiki page sort key: Connected space#SingerThorpe
page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Book-3ASingerThorpe

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY1bbe6dcc54fe323ab081f69041db1b78
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Connected space Path-connected space
wiki page sort key: Connected space# QUERY1bbe6dcc54fe323ab081f69041db1b78

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY3d1dcb921bdec1d85e66aae4e202c777
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Connected space Path-connected space
wiki page sort key: Connected space# QUERY3d1dcb921bdec1d85e66aae4e202c777

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY95328eefbf6da5fc6297c154756ab79c
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Connected space Simply connected space
wiki page sort key: Connected space# QUERY95328eefbf6da5fc6297c154756ab79c

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY4ccf2490399936febcef16b437ebc879
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Connected space Simply connected space
wiki page sort key: Connected space# QUERY4ccf2490399936febcef16b437ebc879

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY97e8f8d5e1d0f90ec9984e53922ed722
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Connected space Contractible space
wiki page sort key: Connected space# QUERY97e8f8d5e1d0f90ec9984e53922ed722

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY833f4694879b31aad952f2e0cedc6b44
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Connected space Contractible space
wiki page sort key: Connected space# QUERY833f4694879b31aad952f2e0cedc6b44

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERYcf8e68e9b7f0633310d518c754ac81d6
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Connected space Irreducible space
wiki page sort key: Connected space# QUERYcf8e68e9b7f0633310d518c754ac81d6

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY0d1fd9fbfe78c34e8c8e3187c8ad35e2
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Connected space Irreducible space
wiki page sort key: Connected space# QUERY0d1fd9fbfe78c34e8c8e3187c8ad35e2

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERYab4633c90a2fddec65cbde8a490370ef
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Connected space Ultraconnected space
wiki page sort key: Connected space# QUERYab4633c90a2fddec65cbde8a490370ef

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY672bdeb5b1402e98746d94fb795580e1
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Connected space Ultraconnected space
wiki page sort key: Connected space# QUERY672bdeb5b1402e98746d94fb795580e1

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY2a92b738476686d0078d421ffd3cac34
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Space with finitely many connected components Connected space
wiki page sort key: Connected space# QUERY2a92b738476686d0078d421ffd3cac34

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERYa1752d08905bc6deed94d36382c934ee
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Space with finitely many connected components Connected space
wiki page sort key: Connected space# QUERYa1752d08905bc6deed94d36382c934ee

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERYe5a87138519dc76d3f8a42c359b339dd
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Space with finitely many quasicomponents Connected space
wiki page sort key: Connected space# QUERYe5a87138519dc76d3f8a42c359b339dd

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY8f05ef8ef2e7847885cd025bbacd2962
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Space with finitely many quasicomponents Connected space
wiki page sort key: Connected space# QUERY8f05ef8ef2e7847885cd025bbacd2962

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY4016df2363acc5572055dc5a0bbd44fd
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Space in which all connected components are open Connected space
wiki page sort key: Connected space# QUERY4016df2363acc5572055dc5a0bbd44fd

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERYb21dea8d1e968be671d2685ded52395c
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Space in which all connected components are open Connected space
wiki page sort key: Connected space# QUERYb21dea8d1e968be671d2685ded52395c

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERY3a3764fa635bebb7b4ab1937228d16dd
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Space in which the connected components coincide with the quasicomponents Connected space
wiki page sort key: Connected space# QUERY3a3764fa635bebb7b4ab1937228d16dd

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_space-23_QUERYb3fb25e6a7b00b60a709915fe49e622a
type: Subject
master page: Connected space
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Space in which the connected components coincide with the quasicomponents Connected space
wiki page sort key: Connected space# QUERYb3fb25e6a7b00b60a709915fe49e622a

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

Line with two origins
type: Subject
page: https://topospaces.subwiki.org/wiki/Line_with_two_origins
wiki namespace: 0
wiki page content language: en
satisfies property: Connected space
wiki page sort key: Line with two origins

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

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

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

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

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

Path-connected space
type: Subject
page: https://topospaces.subwiki.org/wiki/Path-2Dconnected_space
wiki namespace: 0
wiki page content language: en
variation of: Connected space
wiki page sort key: Path-connected space

Locally path-connected space
type: Subject
page: https://topospaces.subwiki.org/wiki/Locally_path-2Dconnected_space
wiki namespace: 0
wiki page content language: en
variation of: Connected space
wiki page sort key: Locally path-connected space

Space with finitely many connected components
type: Subject
page: https://topospaces.subwiki.org/wiki/Space_with_finitely_many_connected_components
wiki namespace: 0
wiki page content language: en
weaker than: Connected space
wiki page sort key: Space with finitely many connected components

Space in which all connected components are open
type: Subject
page: https://topospaces.subwiki.org/wiki/Space_in_which_all_connected_components_are_open
wiki namespace: 0
wiki page content language: en
weaker than: Connected space
wiki page sort key: Space in which all connected components are open

Space in which the connected components coincide with the quasicomponents
type: Subject
page: https://topospaces.subwiki.org/wiki/Space_in_which_the_connected_components_coincide_with_the_quasicomponents
wiki namespace: 0
wiki page content language: en
weaker than: Connected space
wiki page sort key: Space in which the connected components coincide with the quasicomponents

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_product-2Dclosed-23_a38a971fb8fb397c20c119b5f71be65b
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_product-2Dclosed
wiki namespace: 0
wiki page sort key: Connectedness is product-closed#Connected space;1# a38a971fb8fb397c20c119b5f71be65b
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_continuous_image-2Dclosed-23_a38a971fb8fb397c20c119b5f71be65b
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_continuous_image-2Dclosed
wiki namespace: 0
wiki page sort key: Connectedness is continuous image-closed#Connected space;1# a38a971fb8fb397c20c119b5f71be65b
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_not_implies_path-2Dconnected-23_f384efe600eac9e47e0210492e16eac7
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_not_implies_path-2Dconnected
wiki namespace: 0
wiki page sort key: Connected not implies path-connected#Connected space# f384efe600eac9e47e0210492e16eac7
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_not_implies_locally_connected-23_f384efe600eac9e47e0210492e16eac7
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_not_implies_locally_connected
wiki namespace: 0
wiki page sort key: Connected not implies locally connected#Connected space# f384efe600eac9e47e0210492e16eac7
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Path-2Dconnected_implies_connected-23_0c24f04476010f89a7662b636a82fa85
type: Subject
master page: Path-connected implies connected
wiki namespace: 0
wiki page sort key: Path-connected implies connected#Connected space;2# 0c24f04476010f89a7662b636a82fa85
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Irreducible_implies_connected-23_0c24f04476010f89a7662b636a82fa85
type: Subject
master page: Irreducible implies connected
wiki namespace: 0
wiki page sort key: Irreducible implies connected#Connected space;2# 0c24f04476010f89a7662b636a82fa85
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_connected_union-2Dclosed-23_a38a971fb8fb397c20c119b5f71be65b
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_connected_union-2Dclosed
wiki namespace: 0
wiki page sort key: Connectedness is connected union-closed#Connected space;1# a38a971fb8fb397c20c119b5f71be65b
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_closure-2Dpreserved-23_a38a971fb8fb397c20c119b5f71be65b
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_closure-2Dpreserved
wiki namespace: 0
wiki page sort key: Connectedness is closure-preserved#Connected space;1# a38a971fb8fb397c20c119b5f71be65b
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_not_box_product-2Dclosed-23_a38a971fb8fb397c20c119b5f71be65b
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_not_box_product-2Dclosed
wiki namespace: 0
wiki page sort key: Connectedness is not box product-closed#Connected space;1# a38a971fb8fb397c20c119b5f71be65b
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_and_T1_with_at_least_two_points_implies_infinite-23_0c24f04476010f89a7662b636a82fa85
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connected_and_T1_with_at_least_two_points_implies_infinite
wiki namespace: 0
wiki page sort key: Connected and T1 with at least two points implies infinite#Connected space;2# 0c24f04476010f89a7662b636a82fa85
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_not_hereditary-23_a38a971fb8fb397c20c119b5f71be65b
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_not_hereditary
wiki namespace: 0
wiki page sort key: Connectedness is not hereditary#Connected space;1# a38a971fb8fb397c20c119b5f71be65b
page: Connected space

http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_not_weakly_hereditary-23_a38a971fb8fb397c20c119b5f71be65b
type: Subject
master page: http://topospaces.subwiki.org/wiki/Special:URIResolver/Connectedness_is_not_weakly_hereditary
wiki namespace: 0
wiki page sort key: Connectedness is not weakly hereditary#Connected space;1# a38a971fb8fb397c20c119b5f71be65b
page: Connected space

Path-connected implies connected
type: Subject
page: https://topospaces.subwiki.org/wiki/Path-2Dconnected_implies_connected
wiki namespace: 0
wiki page content language: en
proves property satisfaction of: Connected space
wiki page sort key: Path-connected implies connected

Irreducible implies connected
type: Subject
page: https://topospaces.subwiki.org/wiki/Irreducible_implies_connected
wiki namespace: 0
wiki page content language: en
proves property satisfaction of: Connected space
wiki page sort key: Irreducible implies connected

Locally compact and connected with more than one point implies resolvable
type: Subject
page: https://topospaces.subwiki.org/wiki/Locally_compact_and_connected_with_more_than_one_point_implies_resolvable
wiki namespace: 0
wiki page content language: en
uses property satisfaction of: Connected space
wiki page sort key: Locally compact and connected with more than one point implies resolvable

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

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

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

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