O-minimal version of Whitney's extension theorem

Krzysztof Kurdyka, and Wiesław Pawłucki. "O-minimal version of Whitney's extension theorem." Studia Mathematica 224.1 (2014): 81-96. <http://eudml.org/doc/286209>.

@article{KrzysztofKurdyka2014,
abstract = {This is a generalized and improved version of our earlier article [Studia Math. 124 (1997)] on the Whitney extension theorem for subanalytic $^\{p\}$-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 $^\{p\}$-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.},
author = {Krzysztof Kurdyka, Wiesław Pawłucki},
journal = {Studia Mathematica},
keywords = {Whitney field; o-minimal structure},
language = {eng},
number = {1},
pages = {81-96},
title = {O-minimal version of Whitney's extension theorem},
url = {http://eudml.org/doc/286209},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Krzysztof Kurdyka
AU - Wiesław Pawłucki
TI - O-minimal version of Whitney's extension theorem
JO - Studia Mathematica
PY - 2014
VL - 224
IS - 1
SP - 81
EP - 96
AB - This is a generalized and improved version of our earlier article [Studia Math. 124 (1997)] on the Whitney extension theorem for subanalytic $^{p}$-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 $^{p}$-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.
LA - eng
KW - Whitney field; o-minimal structure
UR - http://eudml.org/doc/286209
ER -