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Zero sets of smooth functions in the Pfaffian closure of an o-minimal structure
Author(s):
G.
O.
Jones
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4019-4025.
MSC (2000):
Primary 03C64;
Secondary 58A35
Posted:
June 4, 2008
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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
DOI:
10.1090/S0002-9939-08-09373-8
PII:
S 0002-9939(08)09373-8
Received by editor(s):
July 23, 2007,
Received by editor(s) in revised form:
October 5, 2007
Posted:
June 4, 2008
Additional Notes:
The author is supported by NSERC
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.
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