Whitney's extension theorem in o-minimal structures
Volume 119 / 2017
Annales Polonici Mathematici 119 (2017), 49-67
MSC: Primary 03C64; Secondary 14P10, 32B20.
DOI: 10.4064/ap3940-2-2017
Published online: 20 March 2017
Abstract
In 1934, H. Whitney gave a necessary and sufficient condition on a jet of order $m$ on a closed subset of $E$ of $\mathbb R^n$ to be the jet of order $m$ of a $C^m$-function. Later, K. Kurdyka and W. Pawłucki proposed a subanalytic version of this theorem. In this paper, we work in an o-minimal expansion of a real closed field and prove a definable version of Whitney’s Extension Theorem.
