1Laboratoire de Mathématiques Université de Savoie Campus Scientifique 73376 Le Bourget-du-Lac Cedex, France 2Instytut Matematyki Uniwersytet Jagielloński Łojasiewicza 6 30-348 Kraków, Poland
Studia Mathematica, Tome 224 (2014) no. 1, pp. 81-96
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.
Keywords:
generalized improved version earlier article studia math whitney extension theorem subanalytic mathcal p whitney fields finite version consider whitney fields definable arbitrary o minimal structure real closed field obtain extension which nbsp mathcal p function definable o minimal structure whitney fields consider defined locally closed definable subset local version theorem included
Affiliations des auteurs :
Krzysztof Kurdyka
1
;
Wiesław Pawłucki
2
1
Laboratoire de Mathématiques Université de Savoie Campus Scientifique 73376 Le Bourget-du-Lac Cedex, France
2
Instytut Matematyki Uniwersytet Jagielloński Łojasiewicza 6 30-348 Kraków, Poland
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Krzysztof Kurdyka; Wiesław Pawłucki. O-minimal version of Whitney's extension theorem. Studia Mathematica, Tome 224 (2014) no. 1, pp. 81-96. doi: 10.4064/sm224-1-4
