# Smooth approximation theorem for differential manifolds

Let $M$ and $N$ be differential manifolds and define $C^0(M,N)$ to be the space of all continuous maps from $M$ to $N$, endowed with the compact-open topology. Let $C^\infty(M,N)$ be the space of all smooth maps from $M$ to $N$, viewed as a subset of $C^0(M,N)$. Then $C^\infty(M,N)$ is dense in $C^0(M,N)$.