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Preprint Number 627
627. A. Thamrongthanyalak Definable smoothing of continuous functions Email: Submission date: 22 September 2013. Abstract: Let R be an ominimal expansion of a real closed field. Given definable continuous functions f : U → R and ε : U → (0, +∞), where U is an open subset of R^n, we construct a definable C^mfunction g: U → R with g(x)f(x) < ε(x) for all x ∈ U. Moreover, we show that if f is uniformly continuous, then g can also chosen to be uniformly continuous. Mathematics Subject Classification: 03C64 Keywords and phrases: Full text: pdf.

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