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A Hausdorff topological space is called extremally disconnected if the closure of every open set in it is open. 

A Hausdorff topological space $X$ is a normal space if, given any disjoint closed sets $E$ and $ F$, there are neighbourhoods $U$ of $E$ and $V$ of $F$ that are also disjoint. 

Is it true that every extremally disconnected space is a normal space?

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  • $\begingroup$ $\pi$-Base gives this counterexample for a $T_2$ space which is extremally disconnected but not normal. $\endgroup$ – user228113 Mar 22 '17 at 8:04

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