O-minimal version of Whitney's extension theorem
Volume 224 / 2014
Studia Mathematica 224 (2014), 81-96
MSC: Primary 14P10; Secondary 32B20, 03C64, 14P15.
DOI: 10.4064/sm224-1-4
Abstract
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.
