Definable retractions over Henselian valued fields with analytic\n structure

2019/01/28 by Krzysztof Jan Nowak, Nowak, Krzysztof Jan
Mathematics · #Advanced Topology and Set Theory #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1901.09922

Abstract

Let K be a Henselian, non-trivially valued field with separated analytic\nstructure. We prove the existence of definable retractions onto an arbitrary\nclosed definable subset of Kⁿ. Hence directly follow definable\nnon-Archimedean versions of the extension theorems by Tietze--Urysohn and\nDugundji. This generalizes our previous paper dealing with complete\nnon-Archimedean fields with separated power series and remains true for\nHenselian valued fields with strictly convergent analytic structure, because\nevery such a structure can be extended in a definitional way to a separated\nanalytic structure. Our proof uses a variant of the one from that paper, based\non canonical resolution of singularities, and a model-theoretic compactness\nargument.\n

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• Definable retractions and a non-Archimedean Tietze--Urysohn theorem over Henselian valued fields
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