Let $M$ and $N$ be smooth manifolds, equipped with their underlying manifold topologies. Suppose $F: M \to N$ is a diffeomorphism, meaning that $F$ is a bijective smooth map and its inverse function $F^{-1}: N \to M$ is smooth. Then $F$ is a homeomorphism from the underlying [topological space](/page/Topological%20Space) of $M$ to the underlying topological space of $N$.