几乎处处最好覆盖与最好覆盖

Almost everywhere best coverings and best coverings

得到满足开集条件的自相似集的几乎处处最好覆盖为最好覆盖的几个充分条件以及直线上一类自相似集存在最好覆盖的一个充要条件。所得结论部分回答了[周作领,冯力.关于Hausdorff测度的精确值和拓扑熵的十二个开问题:一个最新结论的概述,非线性。2004,17(2):493-502.]中提出的一些公开问题。最后,作为对本文主要结论的应用,给出了两个例子。

This paper presents some sufficient conditions for an almost everywhere best covering to be a best one for the self similar set satisfying the open set condition and a necessary and sufficient condition for a class of self similar sets defined on real line to have best coverings. The presented results partly answer some open problems in [zhou zuoling, Feng Li. Twelve Open problems on the Exact Value of the Hausdorff Measure and on Topological Entropy： A Brief suney of Recent Results. Nonlinearity, 2004,17 （2）：493- 502-]. As applications,tuo examples are given at the end of this paper.