Kuratowski's Closure-Complement Problem/Exterior

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


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

Proof
By definition, the exterior of $A$ in $\R$ can be defined either as:
 * the complement of the closure of $A$ in $\R$: $A^{- \, \prime}$

or as:
 * the interior of the complement of $A$ in $\R$: $A^{\prime \, \circ}$

From Kuratowski's Closure-Complement Problem: Closure:

It follows by inspection that: