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• W3103673959 abstract "Kirszbraun's Theorem states that every Lipschitz map $Stomathbb R^n$, where $Ssubseteq mathbb R^m$, has an extension to a Lipschitz map $mathbb R^m to mathbb R^n$ with the same Lipschitz constant. Its proof relies on Helly's Theorem: every family of compact subsets of $mathbb R^n$, 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." @default.
• W3103673959 created "2020-11-23" @default.
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• W3103673959 date "2010-10-26" @default.
• W3103673959 modified "2023-10-17" @default.
• W3103673959 title "Definable versions of theorems by Kirszbraun and Helly" @default.
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• W3103673959 doi "https://doi.org/10.1112/plms/pdq029" @default.
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