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Blowing-Up and Whitney (a)-Regularity

Published online by Cambridge University Press:  20 November 2018

Tzee-Char Kuo
Affiliation:
Department of Pure Mathematics University of Sydney Sydny, NSW 2006, Australia
David J. A. Trotman
Affiliation:
Université de Paris-Sud, Mathématiques Bâtement 425 91405, Orsay Cedex, France
Li Pei Xin
Affiliation:
Mathematics Institute Academia Sinica Beijing, China
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Abstract

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When a pair of adjacent C1 strata (X, Y) is Whitney (a)- regular at a point , there is, up to homeomorphism, just one germ at 0 of intersections S ∩ X where S is a Lipschitz transversal to Y at 0 (S is the graph of a Lipschitz map from The proof uses a blowing-up construction and a strong form of Verdier's (w)-regularity.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1989

References

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4. Verdier, J.-L., Stratifications de Whitney et théorème de Bertini-Sard, Inventiones Math. 36 (1976), 265312.Google Scholar