Definable versions of theorems by Kirszbraun and Helly

Matthias Aschenbrenner, Andreas Fischer

Kirszbraun's Theorem states that every Lipschitz map $S\to {\mathbb{R}}^n$, where $S\subseteq {\mathbb{R}}^m$, has an extension to a Lipschitz map ${\mathbb{R}}^m\to {\mathbb{R}}^n$ with the s…