直线上子集的Hs-拓扑及其应用
THE Hs-TOPOLOGY ON A SUBSET IN REAL LINE AND ITS APPLICATIONS

本文利用s-维Hausdorff测度给出了直线上一个子集E上的Hs拓扑和Hs-连通度的定义.讨论了它们的性质及其应用，解决了紧的s-集在欧氏拓扑下往往不连通的问题.
In this paper,by using the s-dimensional Hausdorff measure,we give the concepts of Hs-Topology and Hs-connectivity on a subset in real line,discuss their properties and some applications.In addition,the disconnected problem of a compact s-set under the Euclidean topology is solved