Kuratowski's Closure-Complement Problem/Interior of Complement of Interior of Closure

Theorem
The interior of the complement of the interior of the closure of $A$ in $\R$ is given by:


 * Kuratowski-Closure-Complement-Theorem-IntCompIntClos.png

Proof
From Kuratowski's Closure-Complement Problem: Interior of Closure:

By inspection:

From Interior of Closed Real Interval is Open Real Interval:
 * $\left({\gets \,.\,.\, 0}\right]^\circ = \left({\gets \,.\,.\, 0}\right)$

and:
 * $\left[{2 \,.\,.\, 4}\right]^\circ = \left({2 \,.\,.\, 4}\right)$

and:
 * $\left[{5 \,.\,.\, \to}\right)^\circ = \left({5 \,.\,.\, \to}\right)$