Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 626

Preprint Number 626

Previous Next Preprint server

626. A. Thamrongthanyalak
Whitney's Extension Theorem in o-minimal structures

Submission date: 22 September 2013.


In 1934, Whitney gave a necessary and sufficient condition on a jet of order m on a closed subset E of euclidean space to be the jet of order m of an m-times continuously differentiable function; jets satisfying this condition are known as C^m-Whitney fields. Later, Pawlucki and Kurdyka proved that subanalytic C^m-Whitney fields are jets of order m of sybanalytic C^m-functions. Here, we work in an o-minimal expansion of a real closed field and prove a definable version of Whitney's Extension Theorem: every definable C^m-Whitney field is a jet of order m of a definable C^m-function.

Mathematics Subject Classification: 03C64

Keywords and phrases:

Full text: pdf.

Last updated: March 23 2021 10:22 Please send your corrections to: