Interior is Subset of Exterior of Exterior

Theorem
Let $T$ be a topological space.

Let $H \subseteq T$.

Let $H^e$ denote the exterior of $H$, and let $H^\circ$ denote the interior of $H$.

Then:
 * $H^\circ \subseteq \left({H^e}\right)^e$

Also see

 * Interior may not equal Exterior of Exterior