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Bifurcation sets of definable functions in o-minimal structures
Author(s):
Jesús
Escribano
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2419-2424.
MSC (2000):
Primary 03C64;
Secondary 58C25
Posted:
February 4, 2002
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Abstract:
In this work we answer a question stated by Loi and Zaharia concerning trivialization of definable functions off the bifurcation set: we prove that definable functions are trivial off the bifurcation set, and the trivialization can be chosen definable.
References:
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- 2.
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- M. Coste: An introduction to o-minimal geometry, Dottorato di Ricerca in Matematica, Dip. Mat. Univ. Pisa, Instituti Editoriali e Poligrafici Internazionali (2000).
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- J. Escribano: Trivialidad definible de familias de aplicaciones definibles en estructuras o-minimales, Ph. D. dissertation, Universidad Complutense de Madrid (2000). Also available at http://www.ucm.es/info/dsip/directorio/Personales/jemweb/escriban.html.
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- 10.
- T. L. Loi, A. Zaharia: Bifurcation sets of functions definable in o-minimal structures, Illinois Journal of Mathematics, Vol. 42, Num. 3, Fall 1998. MR 99f:58023
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 4 (1990), 681-689. MR 92c:32046
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Additional Information:
Jesús
Escribano
Affiliation:
Departamento de Sistemas Informáticos y Programación, Facultad de CC. Matemáticas, Universidad Complutense, E-28040 Madrid, Spain
Email:
escribano@sip.ucm.es
DOI:
10.1090/S0002-9939-02-06327-X
PII:
S 0002-9939(02)06327-X
Received by editor(s):
February 2, 2001
Received by editor(s) in revised form:
February 28, 2001 and March 12, 2001
Posted:
February 4, 2002
Additional Notes:
The author was partially supported by DGICYT, PB98-0756-C02-01
Communicated by:
Carl G. Jockusch, Jr.
Copyright of article:
Copyright
2002,
American Mathematical Society
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