Lipschitz extensions of definable p-adic functions
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 function $f : X \times Y \to \mathbb{Q}_p^s$, where $X\subset \mathbb{Q}_p$ and $Y \subset \mathbb{Q}_p^r$, that is $\lambda$-Lipschitz in the first variable, extends to a definable function $\tilde{f}:\mathbb{Q}_p\times Y \to \mathbb{Q}_p^s$ that is $\lambda$-Lipschitz in the first variable.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2014
- DOI:
- 10.48550/arXiv.1402.3465
- arXiv:
- arXiv:1402.3465
- Bibcode:
- 2014arXiv1402.3465K
- Keywords:
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- Mathematics - Logic
- E-Print:
- 11 pages