Let \(X\) be a topological space . A subset \(A\subseteq X\) is open if and only if \(\Int A = A\).
Proof
Due to (0x677a95f6) we have \(\Int A \subseteq A\). But since \(A\) is open we also have \(A\subseteq \Int A\).
On the contrary \(A\) is open since \(\Int A\) is open.