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Ultraconnected space : ウィキペディア英語版 | Ultraconnected space In mathematics, a topological space is said to be ultraconnected if no pair of nonempty closed sets of is disjoint. Equivalently, a space is ultraconnected if and only if the closures of two distinct points always have non trivial intersection. Hence, no space with more than 1 point is ultraconnected.〔Steen and Seeback, Sect. 4〕 All ultraconnected spaces are path-connected (but not necessarily arc connected〔Steen and Seeback, Sect. 4〕), normal, limit point compact, and pseudocompact. ==Notes==
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