  Let $f:M^m\to N^n$ be a smooth map between two differential manifolds with
$N$ connected, $f(M)$ closed and $f(M)\neq N$. In this short note, we show that
either all the points of $M$ are critical points of $f$ or the dimension the
collection of all critical points of $f$ is not less than $n-1$. Some
consequences of this result for surjectivity of mappings are also presented.
