nLab critical point

Context

Differential geometry

differential geometry

synthetic differential geometry

Contents

Definition

For $f : X \to Y$ a smooth function, a critical point is a point $x \in X$ at which the derivative $d X : T X \to T Y$ vanishes.

The collection of all critical points is also called the critical locus of $f$.

A formalization of this in cohesive geometry is at cohesive (infinity,1)-topos – infinitesimal cohesion – critical locus.

Applications

Revised on October 8, 2015 06:54:42 by Urs Schreiber (195.37.209.180)