Closure of Complement of Closure is Regular Closed

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Theorem

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A \subseteq S$ be a subset of $T$.

Let $A^-$ denote the closure of $A$ in $T$.

Let $A'$ denote the complement of $A$ in $S$: $A' = S \setminus A$.


Then $A^{- ' -}$ is regular closed.


Proof