Real Algebraic and Analytic Geometry
Submission: 2007, January 31.
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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