A DEFINABLE P-ADIC ANALOGUE OF KIRSZBRAUN’S THEOREM ON EXTENSIONS OF LIPSCHITZ MAPS

URN to cite this document:: urn:nbn:de:bvb:355-epub-410781
DOI to cite this document:: 10.5283/epub.41078

Cluckers, Raf ; Martin, Florent

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Date of publication of this fulltext: 22 Nov 2019 10:36

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Abstract

A direct application of Zorn's Lemma gives that every Lipschitz map f : X subset of Q(p)(n) -> Q(p)(l) has an extension to a Lipschitz map (f) over tilde : Q(p)(n) -> Q(p)(l). This is analogous, but more easy, to Kirszbraun's Theorem about the existence of Lipschitz extensions of Lipschitz maps S subset of R-n -> R-l. Recently, Fischer and Aschenbrenner obtained a definable version of ...