I'm looking for a proof of this fact - which a professor stated during lesson - concerning smooth compact support functions:
"Let $[a,b] \subset \mathbb{R} $ and $C^\infty_{c}((a,b))$ the set of $C^\infty$ functions $(a,b)\rightarrow \mathbb{R}$ with compact support and
$C_0[a,b])$ the set of continuous functions from $[a,b] \to \mathbb{R}$.
Then exists a sequence of $v_{n} \in C^\infty_{c}((a,b))$ such that for every compact $K \subset (a,b)$ $v_n$ tends uniformly to $v$"
Anyone knows a proof of this fact?
Thanks for the help.