Show that if $f \in C^0(E)$ and $E$ is compact, then $f$ is uniformly continuous. (\textit{Hint}: use the fact that every compact set can be covered by a finite number of balls, $B_\delta (x_i)$. Argue that you can choose the balls so that for each $y\in B_{2\delta}(x_i)$,$|f(y)-f(x_i)|