粗糙集中的软拓扑结构及其性质  

Soft Topology and Its Properties in Rough Set

作　　者：钟满田[1] Zhong Mantian(Education Department of Luoding Polytechnic,Luoding,Guangdong 527200,China)

机构地区：[1]罗定职业技术学院教育系

出　　处：《伊犁师范学院学报（自然科学版）》2019年第4期13-19,共7页Journal of Yili Normal University：Natural Science Edition

基　　金：广东省教育厅2017年度人文社科特色创新类项目“基于工匠传统的高职师范生实践性知识培育研究”(2017GWTSCX050)

摘　　要：为探究粗糙集中的软拓扑结构及其性质,以粗糙集、软拓扑结构为研究对象,采用文献研究法、数学方法、探索性研究法,先定义粗糙集中的软集、软子集、软点等,然后讨论粗糙集中软开集、软Τ0-Τ4空间及其之间的关系和性质,得到粗糙集中存在软开邻域和软开邻域系、软开集和软闭集、软拓扑空间为软正则空间和软正规空间、软拓扑空间为软Τ0-Τ4空间以及Τ3⇒Τ2⇒Τ1⇒Τ0的结论.该结论推广了粗糙集中已有的拓扑结构研究.In order to explore the properties of the soft topological structure which is in the rough set,in this thesis,the rough set and the soft topology are used as the research object,using literature research method,mathematical method and exploratory research method,first we define the rough set of soft sets,soft subsets,soft points,etc,then we discuss the rough set of soft-open set,softΤ0-Τ4 space and their relationship and property,and reach the conclusions that soft open neighborhood and soft open neighborhood,soft open set and soft closed set,soft topological space is soft regular space and soft normal space,soft topological space is softΤ0-Τ4 space andΤ3⇒Τ2⇒Τ1⇒Τ0 all of those are exist in rough set,the conclusion promote the study of the existing research on topology of rough set.

关 键 词：粗糙集 软拓扑结构 开邻域 软开邻域系 软开集 软闭集 

分 类 号：O189.2[理学—数学]