Regular value

For a smooth map $F:M\to N$, a point $y\in N$ is called a regular value if $F$ is a submersion at all points $x\in F^{-1}(\{y\})$. In other words, if the level set at $y$ is regular, or the restriction to the level set is a global submersion.

By this proposition, each level set of a regular value is open.