Interior equals Complement of Closure of Complement

Theorem
Let $T$ be a topological space.

Let $H \subseteq T$.

Let $H^-$ denote the closure of $H$ and $H^\circ$ denote the interior of $H$.

Let $H^\prime$ denote the complement of $H$ in $T$:


 * $H^\prime = T \setminus H$

Then:
 * $H^\circ = H^{\prime \, - \, \prime}$