Interior may not equal Exterior of Exterior

Theorem
Let $T = \struct {S, \tau}$ be a topological space.

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

Let $A^e$ be the exterior of $A$.

Let $A^\circ$ be the interior of $A$.

Then it is not necessarily the case that:
 * $A^{ee} = A^\circ$

Also see

 * Interior is Subset of Exterior of Exterior