Real Algebraic and Analytic Geometry

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183. Andreas Fischer:
Zero-Set Property of O-Minimal Indefinitely Peano Differentiable Functions.


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.

Full text, 11p.: dvi 55k, ps.gz 167k, pdf 207k.

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