Dense subspace of the space of functions vanishing at infinity How can I show that the space of smooth functions with compact support, $C^{\infty}_K$, is dense in the space of continuous functions vanishing at infinity equipped with the supremum norm, $(C_0,|| \cdot ||_{\infty})$ ?
I already know that the space of continuous functions with compact support, $C^0_K$, is dense in $C_0$, so it suffices to show that $C^{\infty}_K$ is dense in $C^0_K$.

Hint: use the theorem of stone-weirstrass
