Smooth approximation of definable continuous functions

Fischer, Andreas

doi:10.1090/S0002-9939-08-09227-7

Smooth approximation of definable continuous functions
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by Andreas Fischer PDF

Proc. Amer. Math. Soc. 136 (2008), 2583-2587 Request permission

Abstract:

Let $\mathcal {M}$ 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.

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