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Preprint Number 1171

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1171. Krzysztof Jan Nowak
Piecewise continuity of functions definable over Henselian rank one valued fields

Submission date: 25 February 2017


Consider a Henselian rank one valued field K of equicharacteristic zero along with the language L^P of Denef--Pas. Let f: A → K be an L^P-definable (with parameters) function on a subset A of K^n. We prove that f is piecewise continuous; more precisely, there is a finite partition of A into L^P-definable locally closed subsets A_1, ... ,A_s of K^n such that the restriction of f to each A_i is a continuous function.

Mathematics Subject Classification: 12J25, 13F30, 14P10

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Full text arXiv 1702.07849: pdf, ps.

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