This is a generalized and improved version of our earlier article [Studia Math. 124 (1997)] on the Whitney extension theorem for subanalytic -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 -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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-1-4,
author = {Krzysztof Kurdyka and Wies\l aw Paw\l ucki},
title = {O-minimal version of Whitney's extension theorem},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {81-96},
zbl = {1318.14052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-1-4}
}
Krzysztof Kurdyka; Wiesław Pawłucki. O-minimal version of Whitney's extension theorem. Studia Mathematica, Tome 223 (2014) pp. 81-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-1-4/