# Critical value

From Diffgeom

## Definition

Let be a smooth map between differential manifolds and . A point is termed a **critical value** for if it satisfies the following condition:

- There exists such that is a critical point; in other words, the map is not surjective. In other words, it is the image of a critical point.
- It is
*not*a regular value of .

is thus partitioned into two subsets: the critical values of , and the regular values of .