How to prove this exercise?
Let $f$ be a continuous function of $\mathbb R^n$ to $\mathbb R^m$, so that $f^{-1}(B)$ is compact in $\mathbb R^n$ for all compact $B$ in $\mathbb R^m$. Prove that $f(A)$ is a closed set in $\mathbb R^m$ for all closed set $A$ in $\mathbb R^n$.