Finite Union of Regular Closed Sets is Regular Closed

Theorem
Let $T$ be a topological space.

Let $n \in \N$.

Suppose that:
 * $\forall i \in \left[{1 .. n}\right]: H_i \subseteq T$

where all the $H_i$ are regular closed in $T$, i.e.:
 * $\forall i \in \left[{1 .. n}\right]: H_i = H_i^{\circ -}$

Then $\displaystyle \bigcup_{i=1}^n H_i$ is regular closed in $T$.

That is:
 * $\displaystyle \bigcup_{i=1}^n H_i = \left({\bigcup_{i=1}^n H_i}\right)^{\circ -}$