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

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


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

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

From Interior of Closed Real Interval is Open Real Interval:
 * $\closedint 0 2^\circ = \openint 0 2$

Hence the result.