# UPC condition with parameter for subanalytic sets

27 Apr 2018 Denkowska Anna Denkowski Maciej P.

In 1986 Paw{\l}ucki and Ple\'sniak introduced the notion of {\sl uniformly polynomially cuspidal} (UPC) sets and proved that every relatively compact and fat subanalytic subset of ${\Rz}^n$ satisfies the UPC condition. Herein we investigate the UPC property of the sections of a relatively compact open subanalytic set $E\subset{\Rz}^k\times{\Rz}^n$ and we show that two of the three parameters in the UPC condition can be chosen independently of the section, while the third one depends generally on the point defining the section...

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