nLab
critical point

Context

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Equality and Equivalence

Contents

Definition

For f:XYf : X \to Y a smooth function, a critical point is a point xXx \in X at which the derivative dX:TXTYd X : T X \to T Y vanishes.

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

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

Applications

Revised on April 21, 2014 06:29:57 by Mike Shulman (108.247.151.163)