An Equivalent Condition for the Self Similar Sets on the Real Line to Have Best Coverings  

作　　者：Jian Dong YIN Zuo Ling ZHOU 

机构地区：[1]Department of Mathematics, Nanchang University [2]Lingnan College, Zhongshan University

出　　处：《Acta Mathematica Sinica,English Series》2013年第9期1637-1646,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundations of China (Grant Nos. 10971236, 11261039)

摘　　要：In this paper, an equivalent condition for the self similar sets on the real line to have best coverings is given. As a result, it partly gives answer to the conjecture which was posed by Zhou and Feng [Zhou, Z. L., Feng, L.： Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17（2）, 493-502 （2004）].In this paper, an equivalent condition for the self similar sets on the real line to have best coverings is given. As a result, it partly gives answer to the conjecture which was posed by Zhou and Feng [Zhou, Z. L., Feng, L.： Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17（2）, 493-502 （2004）].

关 键 词：Self similar set open set condition upper convex density best covering 

分 类 号：O174.12[理学—数学] O151.21[理学—基础数学]