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.
引用
收藏
页码：64 / 68
页数：5
相关论文
共 50 条
  • [21] On the Morse-Sard Theorem for the Sharp Case of Sobolev Mappings
    Korobkov, Mikhail V.
    Kristensen, Jan
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2014, 63 (06) : 1703 - 1724
  • [22] Regularity at infinity of real mappings and a Morse-Sard theorem
    Dias, L. R. G.
    Ruas, M. A. S.
    Tibar, M.
    JOURNAL OF TOPOLOGY, 2012, 5 (02) : 323 - 340
  • [23] MORSE-SARD THEOREM FOR DELTA-CONVEX CURVES
    Pavlica, D.
    MATHEMATICA BOHEMICA, 2008, 133 (04): : 337 - 340
  • [24] The Morse-Sard theorem in Wn,n (Ω): A simple proof
    van der Putten, Roberto
    BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (05): : 477 - 483
  • [25] A simple proof of the Morse-Sard theorem in Sobolev spaces
    Figalli, Alessio
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (10) : 3675 - 3681
  • [26] Some remarks about the Morse-Sard theorem and approximate differentiability
    Azagra, Daniel
    Garcia-Bravo, Miguel
    REVISTA MATEMATICA COMPLUTENSE, 2020, 33 (01): : 161 - 185
  • [27] Nonsmooth Morse-Sard theorems
    Azagra, D.
    Ferrera, J.
    Gomez-Gil, J.
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 160 : 53 - 69
  • [28] Infinite-dimensional version of Morse theory for Lipschitz functionals
    Klimov, VS
    SBORNIK MATHEMATICS, 2002, 193 (5-6) : 889 - 906
  • [29] Morse-Sard theorem in Sobolev spaces - Optimal transportation problems and applications
    De Pascale, L
    BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2001, 4A (03): : 439 - 442
  • [30] Counterexample to Peano's theorem in infinite-dimensional F′-spaces
    Shkarin, SA
    MATHEMATICAL NOTES, 1997, 62 (1-2) : 108 - 115
12345