Let $\displaystyle U \subseteq R^n$ be an open set. Suppose that the map $\displaystyle h:U \rightarrow R^n$ is a $\displaystyle homeomorphism$ $\displaystyle \underline{onto}$ $\displaystyle R^n$ and is $\displaystyle uniformly$ $\displaystyle continuous$.

Prove that $\displaystyle U=R^n$.