Exterior of Exterior of Union of Adjacent Open Intervals

Theorem
Let $A$ be the union of the two adjacent open intervals:
 * $A := \openint a b \cup \openint b c$

Then:
 * $A^{ee} = \openint a c$

where $A^e$ is the exterior of $A$.

Proof
By definition of exterior, $A^e$ is the complement relative to $\R$ of the closure of $A$ in $\R$.

Thus: