regularly open

Given a topological space $(X,\tau )$, a regularly open set is an open set $A\in \tau$ such that

$$\mathrm{int}\overline{A}=A$$

(the interior of the closure is the set itself).

An example of non regularly open set on the standard topology for $ℝ$ is$A=(0,1)\cup (1,2)$ since $\mathrm{int}\overline{A}=(0,2)$.