Kuratowski's Closure-Complement Problem/Closure of Interior

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


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

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


 * $A^\circ = \left({0 \,.\,.\, 1}\right) \cup \left({1 \,.\,.\, 2}\right)$

From Closure of Union of Adjacent Open Intervals:


 * $A^{\circ \, -} = \left[{0 \,.\,.\, 2}\right]$