# Math Help - Compact Sets

1. ## Compact Sets

Let $A\subset R^n$ be compact and let $B\subset$ C(A,R) be compact. Show that there are an $f_0\in B$ and an $x_0\in A$ such that $g(x)\leq f_0(x_0)$ for all $g\in B$ and $x\in A$

$G:A\times B \to \mathbb{R}$, $(x,f)\mapsto f(x)$ is continuous. Then the statement follows from the fact that $A\times B$ is compact.