I'm stacked in the following problem: suppose $f:M\rightarrow N$ is a $C^k$ map between $C^k$-manifolds, such that $\dim M=\dim N=n>1$; if the singularities of $f$ are isolated, then the map is open.
I've tried to use the fact that in the complement of the singularities $f$ is a submersion, hence is an open map, but I don't know how to extend this to the whole function.
Thank you!