Extension of Lipschitz maps definable in Hensel minimal structures

Krzysztof Jan Nowak

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arXiv · 2204.05900

Extension of Lipschitz maps definable in Hensel minimal structures

Krzysztof Jan Nowak

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Abstract

In this paper, we establish a theorem on extension of Lipschitz maps $f$ definable in Hensel minimal fields $K$. This may be regarded as a definable, non-Archimedean, non-locally compact version of Kirszbraun's extension theorem. We proceed with double induction with respect to the dimensions of the ambient space and of the domain of $f$. To this end, we introduce the concept of a definable open cell package with a skeleton which, along with the concept of a risometry, plays a key role in our induction procedure.

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BibTeX RIS

Krzysztof Jan Nowak. 2022-04-12. Extension of Lipschitz maps definable in Hensel minimal structures. https://arxiv.org/abs/2204.05900

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