Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-08-09373-8
Published electronically: June 4, 2008
MathSciNet review: 2425743
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03C64, 58A35

Retrieve articles in all journals with MSC (2000): 03C64, 58A35


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
Email: gojones@math.mcmaster.ca

DOI: https://doi.org/10.1090/S0002-9939-08-09373-8
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.