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arXiv · 1808.09782

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

Krzysztof Jan Nowak
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Abstract

We prove the existence of definable retractions onto arbitrary closed subsets of $K^{n}$ 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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Krzysztof Jan Nowak. 2018-08-29. Definable retractions and a non-Archimedean Tietze--Urysohn theorem over Henselian valued fields. https://arxiv.org/abs/1808.09782

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