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

被引：17

作者：

Ioffe, A. D. ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 09期

关键词：

stratified set; Fredholm mapping; definable set-valued mapping; rate of surjection; critical value;

D O I：

10.1090/S0002-9939-08-09101-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove three theorems extending Sard's theorem and its infinite dimensional extension due to Smale to set-valued mappings with strati. able graphs. The very concept of a critical value comes from (nonsmooth) variational analysis and turns out to be perfectly compatible with the natural condition de. ning "good" strati. cations (e. g., Whitney strati. cation in the finite dimensional case).

引用

页码：3111 / 3119

页数：9

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