Kuratowski's Closure-Complement Problem/Interior of Closure

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


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

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

From Interior of Closed Real Interval is Open Real Interval:
 * $\left[{0 \,.\,.\, 2}\right]^\circ = \left({0 \,.\,.\, 2}\right)$

and:
 * $\left[{4 \,.\,.\, 5}\right]^\circ = \left({4 \,.\,.\, 5}\right)$

From Interior of Singleton in Real Number Space is Empty:
 * $\left\{ {3} \right\}^\circ = \varnothing$