Definable Versions of Theorems by Kirszbraun and Helly
نویسنده
چکیده
Kirszbraun’s Theorem states that every Lipschitz map S → Rn, where S ⊆ Rm, has an extension to a Lipschitz map Rm → Rn with the same Lipschitz constant. Its proof relies on Helly’s Theorem: every family of compact subsets of Rn, having the property that each of its subfamilies consisting of at most n + 1 sets share a common point, has a non-empty intersection. We prove versions of these theorems valid for definable maps and sets in arbitrary definably complete expansions of ordered fields.
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