# Definition:Extremally Disconnected Space

## 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.