A subset of a finite dimensional normed vector space This was left as an unproved theorem in our class: 
Theroem:  If $X$ is a  finite dimensional normed vector space then each subset $M$ of $X$ is compact if and only if $M$ is closed and bounded.
How do I prove it? I know that $M$ is also finte dimensional and hence complete. So it is bounded.

$Hint$ If $X$ has dimension $n$ then $X$ is  linearly homeomorphic to $\mathbb R^n$.
