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Preprint Number 1159
1159. Krzysztof Jan Nowak Hölder and Lipschitz continuity of functions definable over
Henselian
rank one valued fields E-mail: 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: |

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