Sierpinski地毯上的一类Whitney临界集

A Class of Whitney Critical Sets on Sierpinski Rug

以Sierpinski地毯为例,在其上构造Hausdorff维数为S的一类连通集合,其中S=ln(30+31+…+3n)ln3n,n 1.然后证明这些连通集均为Whitney临界集。从而得到不是Whitney临界集的Sierpinski地毯可以包含Whitney临界集。

A class of connected sets, whose Hausdorff dimension was S=In（30＋3^1＋…＋3n）/In3^n,n≥1 was constructed on the Sierpinski Rug. When n was no less than 1, all the connected sets were Whitney＇ s critical sets. The Sierpinski Rug which was not Whitney＇s critical set could contain Whitney＇ s critical set was given in this paper.