I can't figure out how to solve the following question:
1) Let $M$ and $N$ be $C^k$-manifolds, such that $\dim M = \dim N = n>1$, and let $f:M\rightarrow N$ be a $C^k$-function. Show that if the singularities of $M$ are isolated, then $f$ is an open map.
Remark: I've tried to use without sucess the Inverse Function Theorem and Sard's Theorem.
Thank you for your attention