Definition:Regular Open

Definition

Let $X$ be a topological space.

Let $A \subseteq X$.

Then $A$ is regular open in $X$ iff:

$A = A^{- \circ}$

That is, if $A$ equals the interior of its closure.

Also see

• Regular Closed

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$: Closures and Interiors