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

Ioffe, A.

doi:10.1090/S0002-9939-08-09101-6

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

Proc. Amer. Math. Soc. 136 (2008), 3111-3119

DOI: https://doi.org/10.1090/S0002-9939-08-09101-6

Published electronically: May 1, 2008

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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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