Finite Intersection of Regular Open Sets is Regular Open

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 open in $T$, i.e.:
 * $\forall i \in \left[{1 . . n}\right]: H_i = H_i^{- \circ}$

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

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