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

2018/08/29 by Krzysztof Jan Nowak, Nowak, Krzysztof Jan
Mathematics · #12J25 #14P15 #32B20 #32P05 #54C20 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical and Theoretical Analysis #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1808.09782

openalex publication_date 2018/08/29 · openalex created_date 2018/10/26 · openalex updated_date 2026/07/28

Abstract

We prove the existence of definable retractions onto arbitrary closed subsets of Kⁿ definable over Henselian valued fields K. Hence directly follows non-Archimedian analogues of the Tietze--Urysohn and Dugundji theorems on extending continuous definable functions. The main ingredients of the proof are a description of definable sets due to van den Dries, resolution of singularities and our closedness theorem.

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