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.