Definition:Ultraconnected Space/Definition 2

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Definition

A topological space $T = \left({S, \tau}\right)$ is ultraconnected if and only if the closures of every distinct pair elements of $S$ are not disjoint:

$\forall x, y \in S: \left\{{x}\right\}^- \cap \left\{{y}\right\}^- \ne \varnothing$


Also see

  • Results about ultraconnected spaces can be found here.


Sources