A note on Whitney's critical sets  

作　　者：XILifeng WUMin 

机构地区：[1]DepartmentofMathematics,HubeiUniversity,Wuhan430062,China [2]DepartmentofMathematics,NingboUniversity,Ningbo315211,China

出　　处：《Progress in Natural Science:Materials International》2003年第2期152-156,共5页自然科学进展·国际材料（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No. 10171028);Natural Science Foundation of Zhejiang (No. 101026)

摘　　要：The critical arc is an arc which is the critical set for some differentiable function not constant along the arc. In literature on the topic, the differentiable functions are always increasing along the arc, but in this paper we provide a critical arc such that the corresponding differentiable function could not be increasing along the arc. It is also proved that any self-similar Cantor set of dimension greater than 1 is a generalized Whitney's critical set.The critical arc is an arc which is the critical set for some differentiable function not constant along the arc. In literature on the topic, the differentiable functions are always increasing along the arc, but in this paper we provide a critical arc such that the corresponding differentiable function could not be increasing along the arc. It is also proved that any self-similar Cantor set of dimension greater than 1 is a generalized Whitney's critical set.

关 键 词：FRACTAL fractal dimension Whitney's critical set critical arc. 

分 类 号：O144[理学—数学]