高校应用数学学报B辑
高校應用數學學報B輯
고교응용수학학보B집
APPLIED MATHEMATICS A JOURNAL OF CHINESE UNIVERSITIES
2003年
1期
64-68
,共5页
Hausdorff measure%rank-r%Fréchet differentiable
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.
