Definition:Regular Closed Set

Definition

Let $T$ be a topological space.

Let $A \subseteq T$.

Then $A$ is regular closed in $T$ if and only if:

$A = A^{\circ -}$

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

Also known as

Some sources use the term regularly closed, but this is not used on $\mathsf{Pr} \infty \mathsf{fWiki}$.

Also see

• Definition:Regular Open Set

• Results about regular closed sets can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Closures and Interiors