A+ CATEGORY SCIENTIFIC UNIT

Whitney's extension theorem in o-minimal structures

Volume 119 / 2017

Athipat Thamrongthanyalak 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.

Authors

  • Athipat ThamrongthanyalakDepartment of Mathematics and Computer Science
    Faculty of Science
    Chulalongkorn University
    Bangkok 10400, Thailand
    and
    Department of Mathematics
    The Ohio State University
    231 West 18th Avenue
    Columbus, OH 43212, U.S.A.
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image