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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Zero sets of smooth functions in the Pfaffian closure of an o-minimal structure
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by G. O. Jones PDF
Proc. Amer. Math. Soc. 136 (2008), 4019-4025 Request permission

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
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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
  • Email: gojones@math.mcmaster.ca
  • 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
  • © 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), 4019-4025
  • MSC (2000): Primary 03C64; Secondary 58A35
  • DOI: https://doi.org/10.1090/S0002-9939-08-09373-8
  • MathSciNet review: 2425743