Critical point set is closed

This article gives the statement and possibly proof of a theorem that discusses regular values, critical values, regular points or critical points of a smooth map between differential manifolds

Statement

Let $f:M\to N$ be a smooth map of differential manifolds. Then, the set of critical points of $f$ is a closed subset of $M$; equivalently, the set of regular points of $f$ is an open subset of $M$.