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 $\mathrm{int}\overline{A}=(0,2)$.

Title	regularly open
Canonical name	RegularlyOpen
Date of creation	2013-03-22 12:19:43
Last modified on	2013-03-22 12:19:43
Owner	drini (3)
Last modified by	drini (3)
Numerical id	5
Author	drini (3)
Entry type	Definition
Classification	msc 54-00