Smooth approximation of definable continuous functions
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- by Andreas Fischer
- Proc. Amer. Math. Soc. 136 (2008), 2583-2587
- DOI: https://doi.org/10.1090/S0002-9939-08-09227-7
- Published electronically: February 29, 2008
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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.References
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Bibliographic Information
- Andreas Fischer
- Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada
- Email: el.fischerandreas@web.de
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2583-2587
- MSC (2000): Primary 03C64; Secondary 26E10
- DOI: https://doi.org/10.1090/S0002-9939-08-09227-7
- MathSciNet review: 2390530