Submission date: 14 February 2014.

Abstract:

In this paper, we prove a definable version of Kirszbraun's theorem in a non-Archimedean setting for definable families of functions in one variable. More precisely, we prove that every definable and λ-Lipschitz function f : X \subset Q_p \times Y --> Q_p^s, where Y \subset Q_p^r, extends to a definable function \tilde{f}:Q_p^{r+1}\to Q_p^s that is λ-Lipschitz in the first coordinate.

Mathematics Subject Classification:

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Full text arXiv 1402.3465: pdf, ps.