LIPSCHITZ CONTINUITY PROPERTIES FOR p-ADIC SEMI-ALGEBRAIC AND SUBANALYTIC FUNCTIONS
نویسندگان
چکیده
We prove that a (globally) subanalytic function f : X ⊂ Qp → Qp which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken to be subanalytic. We also prove the analogous result for a subanalytic family of functions fy : Xy ⊂ Qp → Qp depending on p-adic parameters. The statements also hold in a semi-algebraic set-up and also in a finite field extension of Qp. These results are p-adic analogues of results of K. Kurdyka over the real numbers. To encompass the total disconnectedness of p-adic fields, we need to introduce new methods adapted to the p-adic situation.
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