Let $f: X^{n} \to Y^{n}$ smooth function with $X$ compact $n$-manifold. Show that the set of regular value is open and dense in $Y$.

Question

Let $f: X^{n} \to Y^{n}$ smooth function with $X$ compact $n$-manifold, $Y$ $n$-dimensional manifold. Show that the set of regular value is open and dense in $Y$.

Let $\mathcal{R}$ the set of regular value. By Sard's Theorem, $\mathcal{R}$ is dense. The hard part is to show that $\mathcal{R}$ is open.

Some hint? Thank you.