关于Cantor三分集定义方式的一个新进展  

A New Development on the Definition of Cantor Trisection Set

作　　者：徐斌 XU Bin(School of Mathematics and Statistics,Pu’er University,Pu’er Yunnan 665099,China)

机构地区：[1]普洱学院数学与统计学院,云南普洱665099

出　　处：《大学数学》2022年第2期22-26,共5页College Mathematics

基　　金：普洱学院数学与应用数学教学团队项目(2020JXTD108)。

摘　　要：通过对Cantor三分集本质结构进行深刻洞察,并结合结构化方法对Cantor三分集的定义方式进行研究.定义了上的无再生三分族、Cantor三分族等概念,证明了Cantor三分集的一个非三进制数模式的新公式,并证明了一个关于三进制数的新公式.为Cantor三分集的“三进制数定义法”提供了一种严密的理论基础,同时也增进了对Cantor三分集本质结构的认识.Through the deep insight into the essential structure of Cantor trisection set,and combined with the structured method,the definition of Cantor trisection set was further explored.Defined the concepts of non reproducing trisection clan and Cantor trisection clan.A new formula for the non ternary number mode of Cantor trisection set was proved.And proved a new formula about ternary numbers.Thus,the Ternary Number Definition Formula of Cantor trisection set was proved,These results provided a rigorous theoretical support for using ternary number to define the Cantor trisection set.At the same time,Deepened understanding of the essential structure of the Cantor trisection set.

关 键 词：上的三分族 上的无再生三分族 Cantor三分族 Cantor三分集 

分 类 号：O174.2[理学—数学]