| dbo:abstract |
In mathematics, a topological space is said to be ultraconnected if no two nonempty closed sets are disjoint. Equivalently, a space is ultraconnected if and only if the closures of two distinct points always have non trivial intersection. Hence, no T1 space with more than one point is ultraconnected. (en) Ультразв'я́зний про́стір — топологічний простір, який не містить дві непорожні неперетинні замкнені множини. (uk) 在數學上，若在一個拓樸空間中，不存在彼此兩兩不相交的非空閉集，則是一個特連通空間（Ultraconnected space）；與之等價地，一個拓樸空間是特連通空間，當且僅當 其兩個不同的點的閉包之間總有非平凡的交集，因此沒有多於一個點的空間可以是特連通空間。 所有特連通空間的都是道路连通空間（但未必是弧連通空間）、正规空间、（Limit point compact）空間和偽緊緻空間（pseudocompact space）。 (zh) |
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dbr:Limit_point_compact dbr:Mathematics dbr:Normal_space dbr:Sierpiński_space dbr:Pseudocompact_space dbc:Properties_of_topological_spaces dbr:Closed_set dbr:Counterexamples_in_Topology dbr:Hyperconnected_space dbr:Excluded_point_topology dbr:Topological_space dbr:T1_space dbr:Right_order_topology dbr:Arc_connected dbr:Disjoint_(sets) dbr:Indiscrete_topology dbr:Path-connected |
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5814 (xsd:integer) |
| dbp:title |
Ultraconnected space (en) |
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dbt:ISBN dbt:Reflist dbt:PlanetMath_attribution |
| dct:subject |
dbc:Properties_of_topological_spaces |
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yago:Abstraction100002137 yago:Possession100032613 yago:Property113244109 yago:Relation100031921 yago:WikicatPropertiesOfTopologicalSpaces |
| rdfs:comment |
In mathematics, a topological space is said to be ultraconnected if no two nonempty closed sets are disjoint. Equivalently, a space is ultraconnected if and only if the closures of two distinct points always have non trivial intersection. Hence, no T1 space with more than one point is ultraconnected. (en) Ультразв'я́зний про́стір — топологічний простір, який не містить дві непорожні неперетинні замкнені множини. (uk) 在數學上，若在一個拓樸空間中，不存在彼此兩兩不相交的非空閉集，則是一個特連通空間（Ultraconnected space）；與之等價地，一個拓樸空間是特連通空間，當且僅當 其兩個不同的點的閉包之間總有非平凡的交集，因此沒有多於一個點的空間可以是特連通空間。 所有特連通空間的都是道路连通空間（但未必是弧連通空間）、正规空间、（Limit point compact）空間和偽緊緻空間（pseudocompact space）。 (zh) |
| rdfs:label |
Ultraconnected space (en) Ультразв'язний простір (uk) 特連通空間 (zh) |
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freebase:Ultraconnected space yago-res:Ultraconnected space wikidata:Ultraconnected space dbpedia-uk:Ultraconnected space dbpedia-zh:Ultraconnected space https://global.dbpedia.org/id/4wcGa |
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wikipedia-en:Ultraconnected_space?oldid=1115289514&ns=0 |
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wikipedia-en:Ultraconnected_space |
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dbr:Interior_algebra dbr:Hyperconnected_space dbr:Finite_topological_space dbr:Ultraconnected dbr:Ultra-connected |
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wikipedia-en:Ultraconnected_space |