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O-minimal version of Whitney's extension theorem

Tom 224 / 2014

Krzysztof Kurdyka, Wiesław Pawłucki Studia Mathematica 224 (2014), 81-96 MSC: Primary 14P10; Secondary 32B20, 03C64, 14P15. DOI: 10.4064/sm224-1-4

Streszczenie

This is a generalized and improved version of our earlier article [Studia Math. 124 (1997)] on the Whitney extension theorem for subanalytic $\mathcal C^p$-Whitney fields (with $p$ finite). In this new version we consider Whitney fields definable in an arbitrary o-minimal structure on any real closed field $R$ and obtain an extension which is a $\mathcal C^p$-function definable in the same o-minimal structure. The Whitney fields that we consider are defined on any locally closed definable subset of $R^n$. In such a way, a local version of the theorem is included.

Autorzy

  • Krzysztof KurdykaLaboratoire de Mathématiques
    Université de Savoie
    Campus Scientifique
    73376 Le Bourget-du-Lac Cedex, France
    e-mail
  • Wiesław PawłuckiInstytut Matematyki
    Uniwersytet Jagielloński
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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