# Definition:Critical Point (Topology)

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*This page is about Critical Point in the context of topology. For other uses, see Critical Point.*

## Definition

Let $f: X \to Y$ be a smooth map of manifolds.

A point $x \in X$ is called a **critical point** of $f$ if and only if $\d f_x: T_x \sqbrk X \to T_y \sqbrk Y$ is not surjective at $x$.