Critical value - Definition and Overview

In differential topology, a critical value of a differentiable map between differentiable manifolds is the image of a critical point.

The basic result on critical values is Sard's lemma. The set of critical values can be quite irregular; but in Morse theory it becomes important to consider real-valued functions on a manifold M, such that the set of critical values is in fact finite. The theory of Morse functions shows that there are many such functions; and that they are even typical, or generic in the sense of Baire category.

Example Usage of Critical