Prove that a continuous function of compact support defined on $R^n$ is bounded. I am working through a few sets of notes I found on the internet and I came across this exercise. How do I prove that a continuous function $f$ of compact support defined on $R^n$ is bounded?
It seems believable that it is true for $f$ in $R$ because I can visualize it but how do I prove this properly for $R^n$? Any ideas?

Let $K$ be the support of $f$. Since the image of a compact set through a continuous function is compact, $f(K)$ is closed and bounded by the Heine-Borel theorem.
