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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Critical values of set-valued maps with stratifiable graphs. Extensions of Sard and Smale-Sard theorems


Author: A. D. Ioffe
Journal: Proc. Amer. Math. Soc. 136 (2008), 3111-3119
MSC (2000): Primary 49J53, 58K05
Published electronically: May 1, 2008
MathSciNet review: 2407074
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Abstract: We prove three theorems extending Sard's theorem and its infinite dimensional extension due to Smale to set-valued mappings with stratifiable graphs. The very concept of a critical value comes from (nonsmooth) variational analysis and turns out to be perfectly compatible with the natural condition defining ``good'' stratifications (e.g., Whitney stratification in the finite dimensional case).


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Additional Information

A. D. Ioffe
Affiliation: Department of Mathematics, Technion, Haifa 32000, Israel

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09101-6
PII: S 0002-9939(08)09101-6
Keywords: Stratified set, Fredholm mapping, definable set-valued mapping, rate of surjection, critical value
Received by editor(s): June 19, 2006
Published electronically: May 1, 2008
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2008 American Mathematical Society