About closed subsets definable in Hensel minimal structures

Krzysztof Jan Nowak

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arXiv · 2403.08039

About closed subsets definable in Hensel minimal structures

Krzysztof Jan Nowak

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Abstract

The main purpose is to establish two theorems about closed 0-definable subsets $A$ of an affine space $K^{n}$ over a Hensel minimal field $K$. The first, being a non-Archimedean counterpart of one from o-minimal geometry, states that every such subset $A$ is the zero locus of a continuous 0-definable function on $K^{n}$. The second is a definable, non-Archimedean version of the Tietze-Urysohn extension theorem. The proofs use ubiquity of clopen sets in non-Archimedean geometry and a description of definable sets.

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Krzysztof Jan Nowak. 2024-03-12. About closed subsets definable in Hensel minimal structures. https://arxiv.org/abs/2403.08039

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