Let $M$ and $N$ be smooth manifolds, and let $F:M\to N$ be a continuous map. Suppose that for every point $p\in M$ there exist a smooth chart $(U,\varphi)$ of $M$ with $p\in U$ and a smooth chart $(V,\psi)$ of $N$ with $F(p)\in V$ such that $F(U)\subset V$ and the coordinate representation