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A [[topological space]] in which no two non-empty [[closed set|closed subsets]] are disjoint or equivalently the closures of [[singleton]]s are never disjoint.  An ultraconnected space is [[Connected space|connected]] and indeed [[Path-connected space|path-connected]].

See: [[Connectivity]] for references.

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How to Cite This Entry:
Ultraconnected topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ultraconnected_topological_space&oldid=37312

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