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$\mathscr{C}^{p}$-parametrization in O-minimal Structures

Part of: Model theory

Published online by Cambridge University Press:  09 January 2019

Beata Kocel-Cynk ,
Wiesław Pawłucki  and
Anna Valette
Beata Kocel-Cynk
Affiliation:
Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, PL31-155 Cracow, Poland Email: bkocel@usk.pk.edu.pl
Wiesław Pawłucki
Affiliation:
Institute of Mathematics, Jagiellonian University, ul. St. Łojasiewicza 6, PL30-348 Cracow, Poland Email: wieslaw.pawlucki@im.uj.edu.planna.valette@im.uj.edu.pl
Anna Valette
Affiliation:
Institute of Mathematics, Jagiellonian University, ul. St. Łojasiewicza 6, PL30-348 Cracow, Poland Email: wieslaw.pawlucki@im.uj.edu.planna.valette@im.uj.edu.pl
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Abstract

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We give a geometric and elementary proof of the uniform $\mathscr{C}^{p}$-parametrization theorem of Yomdin and Gromov in arbitrary o-minimal structures.

Keywords

o-minimal structureCp-parametrization

MSC classification

Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 14P15: Real analytic and semianalytic sets 32B20: Semi-analytic sets and subanalytic sets
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 1 , March 2019 , pp. 99 - 108
Copyright
© Canadian Mathematical Society 2018 

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