Definition:Extremally Disconnected Space

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Definition

Definition 1

A $T_2$ (Hausdorff) topological space $T = \left({S, \tau}\right)$ is extremally disconnected if and only if the closure of every open set of $T$ is open.


Definition 2

A $T_2$ (Hausdorff) topological space $T = \left({S, \tau}\right)$ is extremally disconnected if and only if the interior of every closed set of $T$ is closed.


Definition 3

A $T_2$ (Hausdorff) topological space $T = \left({S, \tau}\right)$ is extremally disconnected if and only if the closures of every pair of open sets which are disjoint are also disjoint.


Also see

  • Results about extremally disconnected spaces can be found here.