Regular value

Definition

Symbol-free definition

Given a smooth map of differential manifolds, a point in the image manifold is termed a regular value for the smooth map if every point in its inverse image is a regular point, i.e. if the map from the tangent space at any point in the inverse image, is surjective.

Definition with symbols

Let $f:M\to N$ be a smooth map of differential manifolds. A point $p\in N$ is termed a regular value of $f$ if for every $m\in f^{-1}(\{p\})$, the induced map $(df)_{m}:T_{m}M\to T_{p}N$, is surjective.