Definition:Regular Closed Set
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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
- 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