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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Zero sets of smooth functions in the Pfaffian closure of an o-minimal structure

Author: G. O. Jones
Journal: Proc. Amer. Math. Soc. 136 (2008), 4019-4025
MSC (2000): Primary 03C64; Secondary 58A35
Published electronically: June 4, 2008
MathSciNet review: 2425743
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Abstract | References | Similar Articles | Additional Information

Abstract: I show that in an o-minimal structure on the real field, satisfying certain conditions, every closed definable set is the zero set of a smooth definable function. The conditions are shown to hold in the Pfaffian closure of a polynomially bounded o-minimal structure having smooth cell decomposition.

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Additional Information

G. O. Jones
Affiliation: Department of Mathematics and Statistics, McMaster University, 1280 Main Street, West Hamilton, Ontario L8S 4K1, Canada
Address at time of publication: School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom

PII: S 0002-9939(08)09373-8
Received by editor(s): July 23, 2007
Received by editor(s) in revised form: October 5, 2007
Published electronically: June 4, 2008
Additional Notes: The author is supported by NSERC
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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