Let $C$ be a set of all continuous functions that map from a compact set to the reals. Is the set of all polynomials dense in $C$, with respect to the sup metric?
Can I show that by using the Stone-Weierstrauss Theorem? Since I can find a sequence of polynomials that converge uniformly to any continuous function, if I take the closure of the set of polynomials, do I get the entire set of continuous functions?