O-minimal version of Whitney's extension theorem

• Autorzy: Krzysztof Kurdyka , Wiesław Pawłucki
• Języki publikacji: EN

Abstrakty

EN

This is a generalized and improved version of our earlier article [Studia Math. 124 (1997)] on the Whitney extension theorem for subanalytic $𝓒^{p}$-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 $𝓒^{p}$-function definable in the same o-minimal structure. The Whitney fields that we consider are defined on any locally closed definable subset of Rⁿ. In such a way, a local version of the theorem is included.

Kategorie tematyczne

• 32B20: Semi-analytic sets and subanalytic sets
• 14P15: Real analytic and semianalytic sets
• 03C64: Model theory of ordered structures; o-minimality
• 14P10: Semialgebraic sets and related spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 224
• Numer: 1
• Strony: 81-96

Daty

wydano

2014

Twórcy

autor

Krzysztof Kurdyka

• Laboratoire de Mathématiques, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France

autor

Wiesław Pawłucki

• Instytut Matematyki, Uniwersytet Jagielloński, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/sm224-1-4