Real Algebraic and Analytic Geometry

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216. Andreas Fischer:
Smooth Approximation of Definable Continuous Functions.


Submission: 2007, January 31.

Let M be an o-minimal expansion of the real exponential field which possesses smooth cell decomposition. We prove that for every definable open set, the definable indefinitely continuously differentiable functions are a dense subset of the definable continuous function with respect to the o-minimal Whitney topology.

Mathematics Subject Classification (2000): 03C64 26E10.

Keywords and Phrases: o-minimal structures, exponential function, approximation.

Full text, 4p.: dvi 22k, ps.gz 122k, pdf 146k.

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