|
Smooth approximation of definable continuous functions
Author(s):
Andreas
Fischer
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2583-2587.
MSC (2000):
Primary 03C64;
Secondary 26E10
Posted:
February 29, 2008
MathSciNet review:
2390530
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let  be an  -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  -minimal Whitney topology.
References:
-
- 1.
- van den Dries, L., Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series, 248. Cambridge University Press, Cambridge, 1998. MR 1633348 (99j:03001)
- 2.
- van den Dries, L., and Miller, C., Geometric categories and o-minimal structures. Duke Math. J. 84 (1996), no. 2, 497-540. MR 1404337 (97i:32008)
- 3.
- Efroymson, G. A., The extension theorem for Nash functions. Real algebraic geometry and quadratic forms (Rennes, 1981), pp. 343-357, Lecture Notes in Math., 959, Springer, Berlin-New York, 1982. MR 683141 (84i:58002)
- 4.
- Escribano, J., Approximation theorems in o-minimal structures, Illinois Journal of Mathematics 46(1) (2002), 111-128. MR 1936078 (2003i:03042)
- 5.
- Jones, G. O., Local to global methods in o-minimal expansions of fields. Doctoral Thesis, Wolfson College University of Oxford, 2006.
- 6.
- Pecker, D., On Efroymson's extension theorem for Nash functions. J. Pure Appl. Algebra 37 (1985), no. 2, 193-203. MR 796409 (87e:58002)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
03C64,
26E10
Retrieve articles in all Journals with
MSC (2000):
03C64,
26E10
Additional 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
DOI:
10.1090/S0002-9939-08-09227-7
PII:
S 0002-9939(08)09227-7
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
Posted:
February 29, 2008
Additional Notes:
This research was partially supported by the NSERC discovery grant of Dr. Salma Kuhlmann
Communicated by:
Julia Knight
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
