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Preprint Number 1171
1171. Krzysztof Jan Nowak Piecewise continuity of functions definable over Henselian rank one
valued fields E-mail: Submission date: 25 February 2017 Abstract: 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 Keywords and phrases: |

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