|
| 摘要: |
| 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. |
| 关键词: 分形 Hausdorff测度 Hs-拓扑 Hs-连通度 |
| DOI： |
| 分类号:O174.12;O189.11 |
| 基金项目:海南省自然科学基金资助（113003）；国家自然科学基金资助（11461016）. |
|
| THE Hs-TOPOLOGY ON A SUBSET IN REAL LINE AND ITS APPLICATIONS |
|
LONG Lun-hai,LIANG Li,SAN Jia-jun
|
| Abstract: |
| 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. |
| Key words: fractal Hausdorff measure Hs-Topology Hs-connectivity |
