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Bifurcation sets of definable functions in o-minimal structures

Author: Jesús Escribano
Journal: Proc. Amer. Math. Soc. 130 (2002), 2419-2424
MSC (2000): Primary 03C64; Secondary 58C25
Published electronically: February 4, 2002
MathSciNet review: 1897468
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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.

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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

Received by editor(s): February 2, 2001
Received by editor(s) in revised form: February 28, 2001, and March 12, 2001
Published electronically: February 4, 2002
Additional Notes: The author was partially supported by DGICYT, PB98-0756-C02-01
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2002 American Mathematical Society