A COUNTEREXAMPLE TO INFINITE-DIMENSIONAL VERSION OF THE MORSE-SARD THEOREM

被引：0
|
作者：
Jiang HaiyiDept. of Math.
机构：
来源：
Applied Mathematics:A Journal of Chinese Universities | 2003年 / 01期
关键词：
Hausdorff measure; rank-r; Fréchet differentiable;
D O I：
暂无
中图分类号：
O177.9 [];
学科分类号：
070104 ;
摘要：
In this note,a positive answer for a question posed by S.Bates in 1992 is given,i.e.there exists a C∞ rank=1 map f:l2→R1 such that f(A) has nonempty interior for some subset Al2 of critical points with finite Hausdorff dimension.It is to say the Morse criticality theorem can not be generalized to infinite-dimensional spaces.
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页码：64 / 68
页数：5
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