Kuratowski's Closure-Complement Problem/Interior

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


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

Proof
From Interior equals Complement of Closure of Complement:
 * $A^\circ = A^{\prime \, - \, \prime}$

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

It can be determined by inspection that:
 * $A^{\prime \, - \, \prime} = \openint 0 1 \cup \openint 1 2$

Hence the result.