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.
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| - Ultraconnected space (en)
- Ультразв'язний простір (uk)
- 特連通空間 (zh)
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| - 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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| - Ultraconnected space (en)
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| - 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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