Let $X$ be a compact metric space. Let $C_+(X)$ be the set of all non negative continuous functions on $X$. Do there exist a countable dense set of $C_+(X)$?
I think the answer is affirmative. For example when $X=[a,b]$ we can think of rational polynomials and take its absolute values. But I cannot really find an analogous of polynomials for the general compact metric space.