# 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 $x$.

This article, or a section of it, needs explaining.In particular: What are $\d f_x$, $T_x$ and $T_y$ in this context?You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Explain}}` from the code. |