Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry

@article{Cluckers2010ApproximationsAL,
  title={Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry},
  author={R. Cluckers and Immanuel Halupczok},
  journal={Selecta Mathematica},
  year={2010},
  volume={18},
  pages={825-837}
}
  • R. Cluckers, Immanuel Halupczok
  • Published 2010
  • Mathematics
  • Selecta Mathematica
  • It is known that a p-adic, locally Lipschitz continuous semi-algebraic function, is piecewise Lipschitz continuous, where finitely many pieces suffice and the pieces can be taken semi-algebraic. We prove that if the function has locally Lipschitz constant 1, then it is also piecewise Lipschitz continuous with the same Lipschitz constant 1 (again, with finitely many pieces). We do this by proving the following fine preparation results for p-adic semi-algebraic functions in one variable. Any such… CONTINUE READING
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