一类直线上的自相似集的特征  

A Characteristic of Self Similar Set with the Open set Condition in R

作　　者：尹建东[1] 邓中书[2] 

机构地区：[1]南昌大学数学系,江西南昌330031 [2]南昌大学学报编辑部,江西南昌330047

出　　处：《南昌大学学报（理科版）》2010年第3期214-216,220,共4页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学青年基金资助项目(2008GQS0071)

摘　　要：首先得到直线上满足开集条件自相似集的最好形状的一个特征。然后作为应用,证明了对于由直线上的相似压缩个数不大于3的迭代函数系所生成的满足开集条件的自相似集而言,它们的最好覆盖的存在与自然覆盖为最好覆盖等价。In this paper,a characteristic of the self similar sets with the open set condition is firstly gotten.As an appication,for the self similar set E with the open set condition in R,which is induced by an IFS consisting of at most three contracting similarities,E has the best covering if and only if the natural covering of E is the best one,where IFS stands for.

关 键 词：开集条件 自相似集 最好覆盖 自然覆盖 

分 类 号：O174.12[理学—数学]