Extremally Disconnected by Disjoint Open Sets
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Theorem
Let $T = \left({X, \vartheta}\right)$ be a $T_2$ (Hausdorff) topological space.
Then $T$ is extremally disconnected iff the closures of every pair of open sets which are disjoint are also disjoint.
Proof
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Sources
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 4$: Disconnectedness
