Real Algebraic and Analytic Geometry |

Smooth Approximation of Definable Continuous Functions.

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Submission: 2007, January 31.

*Abstract:
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.

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