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Published in:
1995 | OriginalPaper | Chapter
Special Problems
Authors : V. P. Havin, N. K. Nikol’skij
Published in: Commutative Harmonic Analysis III
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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Let f: X → Y be a mapping of smooth manifolds. The point x εX is said to be critical for f, and f(x) is a critical value of / if rang df(x) < dimf(x)Y, In particular an imbedding X ↩Y is critical at all points x εX where the dimension of X is less than the dimension of Y. In §3 of Chapt. 2, we defined the inverse image of any generalized function defined on Y under a submersion f: X → Y, i.e., under a mapping that has no critical points.