\begin{definition}[Definition:Critical Point (Topology)]
Let $f: X \to Y$ be a smooth map of manifolds.
A point $x \in X$ is called a '''critical point''' of $f$ {{iff}} $\d f_x: T_x \sqbrk X \to T_y \sqbrk Y$ is not surjective at $x$.
{{explain|What are $\d f_x$, $T_x$ and $T_y$ in this context?}}
Category:Definitions/Topology
\end{definition}