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ultraconnected space (Definition)

A topological space $X$ is said to be ultraconnected if no pair of nonempty closed sets of $X$ is disjoint.

All ultraconnected spaces are path-connected, normal, limit point compact, and pseudocompact.



"ultraconnected space" is owned by yark.
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See Also: hyperconnected

Other names:  ultra-connected space
Also defines:  ultraconnected, ultra-connected
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Cross-references: pseudocompact, limit point compact, normal, path-connected, disjoint, closed sets, topological space
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This is version 3 of ultraconnected space, born on 2004-04-29, modified 2005-05-30.
Object id is 5814, canonical name is UltraconnectedSpace.
Accessed 4385 times total.

Classification:
AMS MSC: 54D05 (General topology :: Fairly general properties :: Connected and locally connected spaces )
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