A simplified proof of the o-minimal Whitney Extension Theorem

TL;DR

This paper presents a simplified proof of the o-minimal Whitney Extension Theorem, utilizing a new definable variant of Urysohn's lemma for class ^q, making the original proof more accessible.

Contribution

It introduces a simplified proof of the o-minimal Whitney Extension Theorem using a novel definable Urysohn's lemma, enhancing understanding and accessibility.

Findings

Simplified proof of the o-minimal Whitney Extension Theorem

Development of a definable ^q Urysohn's lemma

Improved clarity in o-minimal geometric analysis

Abstract

We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysohn's lemma for class $\mathcal{C}^q$ (see Section 3).