# 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 $\mathbbmss{R}$ is $A=(0,1)\cup(1,2)$ since $\mathrm{int}\overline{A}=(0,2)$.

Title regularly open RegularlyOpen 2013-03-22 12:19:43 2013-03-22 12:19:43 drini (3) drini (3) 5 drini (3) Definition msc 54-00