覆盖空间及粗糙集与拓扑的统一  

Covering Space and the Unification of Rough Sets and Topology

作　　者：张贤勇[1] 熊方[2] 莫智文[1] 

机构地区：[1]四川师范大学基础部,四川成都610110 [2]四川天一学院信息工程系,四川龙泉610100

出　　处：《数学的实践与认识》2006年第11期191-195,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(69803007)

摘　　要：引入覆盖空间,定义了其邻域、内部、闭包、测度等概念,研究了它们的性质.得出了粗糙集近似空间和拓扑空间都是具体覆盖空间的重要结论,从而用覆盖空间统一了粗糙集和拓扑.利用覆盖空间,得到了粗糙集和拓扑中更深刻的性质,从算子论和集合论的角度丰富和深化了粗糙集与拓扑的内容.In this paper covering space is introduced. The notions, neighborhood, interior, closure and measure, are defined, and the properties of them are studied. The important conclusion that the approximate space of rough sets and topology space are specific covering spaces is achieved. So rough sets and topology are unified by covering space. Furthermore the deeper properties of rough sets and topology are achieved by covering spaces, and rough sets theory and topology have been enriched from the operator-oriented and set-oriented views.

关 键 词：粗糙集 拓扑 覆盖空间 近似算子 非经典逻辑 

分 类 号：O159[理学—数学]