Definition For Maps
For a differentiable map f between Rm and Rn, critical points are the points where the differential of f is a linear map of rank less than n; in particular, every point is critical if m < n. This definition immediately extends to maps between smooth manifolds. The image of a critical point under f is a called a critical value. A point in the complement of the set of critical values is called a regular value. Sard's theorem states that the set of critical values of a smooth map has measure zero.
Read more about this topic: Critical Point (mathematics)
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