# Extremally disconnected space is normal

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?

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