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:

Full text arXiv 1702.07849: pdf, ps.