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Proceedings of the American Mathematical Society

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Smooth approximation of definable continuous functions

Author: Andreas Fischer
Journal: Proc. Amer. Math. Soc. 136 (2008), 2583-2587
MSC (2000): Primary 03C64; Secondary 26E10
Published electronically: February 29, 2008
MathSciNet review: 2390530
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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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Andreas Fischer
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada

Keywords: $o$-minimal structures, exponential function, approximation
Received by editor(s): January 31, 2007
Received by editor(s) in revised form: April 10, 2007, and May 15, 2007
Published electronically: February 29, 2008
Additional Notes: This research was partially supported by the NSERC discovery grant of Dr. Salma Kuhlmann
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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