Submission date: 11 February 2017

Abstract:

Consider a Henselian rank one valued field K of equicharacteristic zero with the three-sorted language L of Denef-Pas. Let f: A → K be a continuous L-definable (with parameters) function on a closed bounded subset A ⊆ K^n. The main purpose is to prove that then f is Hölder continuous with some exponent s ≥ 0 and constant c ≥ 0, a fortiori, f is uniformly continuous. Further, if f is locally Lipschitz continuous with a constant c, then f is (globally) Lipschitz continuous with possibly some larger constant d. Also stated are some problems concerning continuous and Lipschitz continuous functions definable over Henselian valued fields.

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

Keywords and phrases:

Full text arXiv 1702.03463: pdf, ps.