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Critical values of set-valued maps with stratifiable graphs. Extensions of Sard and Smale-Sard theorems
Author(s):
A.
D.
Ioffe
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3111-3119.
MSC (2000):
Primary 49J53, 58K05
Posted:
May 1, 2008
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Additional information
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:
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
Posted:
May 1, 2008
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2008,
American Mathematical Society
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