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- W2914211909 abstract "Let $K$ be a Henselian, non-trivially valued field with separated analytic structure. We prove the existence of definable retractions onto an arbitrary closed definable subset of $K^{n}$. Hence directly follow definable non-Archimedean versions of the extension theorems by Tietze--Urysohn and Dugundji. This generalizes our previous paper dealing with complete non-Archimedean fields with separated power series and remains true for Henselian valued fields with strictly convergent analytic structure, because every such a structure can be extended in a definitional way to a separated analytic structure. Our proof uses a variant of the one from that paper, based on canonical resolution of singularities, and a model-theoretic compactness argument." @default.
- W2914211909 created "2019-02-21" @default.
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- W2914211909 date "2019-01-28" @default.
- W2914211909 modified "2023-09-27" @default.
- W2914211909 title "Definable retractions over Henselian valued fields with analytic structure" @default.
- W2914211909 hasPublicationYear "2019" @default.
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