Whitney's example by way of Assouad's embedding

被引：12
作者：
Hajlasz, P
机构：
[1] Univ Warsaw, Inst Math, PL-02097 Warsaw, Poland
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 131卷 / 11期
关键词：
critical set; Whitney's example; Whitney's extension theorem; Van Koch snow flake; Assouad's embedding;
D O I：
10.1090/S0002-9939-03-06913-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we show how to use the Assouad embedding theorem (about almost bi-Lipschitz embeddings) to construct examples of C-m functions which are not constant on a critical set homeomorphic to the n-dimensional cube. This extends the famous example of Whitney. Our examples are shown to be sharp.
引用
收藏
页码：3463 / 3467
页数：5
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