Hi,

is the space $C_0(\mathbb{R}^m)$, $m \in \mathbb{N}$ of continuous functions with compact support separable? If yes: where can I find a proof for that?

Please note: this is not a duplicate of this question (click), since I asked for compact support.

The reason I'm asking is: here (click) the author (L.C. Evans) seems to use the fact on page 18 (page 20 of the pdf) first line without mentioning the difficulty, that $\mathbb{R}$ isn't compact. The entire proof is senseless without this fact.

Your help is very much appreciated! Thanks!