# Definition:Extremally Disconnected Space

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## Definition

### Definition 1

A $T_2$ (Hausdorff) topological space $T = \struct {S, \tau}$ 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 $T = \struct {S, \tau}$ 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 $T = \struct {S, \tau}$ 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.