Zero-set Property of O-minimal Indefinitely Peano Differentiable Functions
نویسنده
چکیده
Given an o-minimal expansion M of a real closed field R which is not polynomially bounded. Let P∞ denote the definable indefinitely Peano differentiable functions. If we further assume that M admits P∞ cell decomposition, each definable closed set A ⊂ Rn is the zero-set of a P∞ function f : Rn → R. This implies P∞ approximation of definable continuous functions and gluing of P∞ functions defined on closed definable sets.
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