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:
 * $\closedint 0 2^\circ = \openint 0 2$

and:
 * $\closedint 4 5^\circ = \openint 4 5$

From Interior of Singleton in Real Number Line is Empty:
 * $\set 3^\circ = \O$