Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2007, January 31.

Abstract:
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 of 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.

Mathematics Subject Classification (2000): 03C64; 49J52.

Keywords and Phrases: o-minimal structure, Peano differentiable functions, zero-set property.

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