A continuous bijection is a homeomorphism exactly when it is open.Suggest a slogan
Let \(f\colon X\to Y\) be a continuous bijection. Then \(f\) is a homeomorphism if and only if \(f\) is an open map, since \(\inverseof{(\inverseof{f})}(U) = f(U)\) for every open \(U\subseteq X\).