拓扑系统中的闭包元和闭包集及其相关性质  

Closure elements and closure sets in topological systems and their related properties

作　　者：高雅[1] 吴洪博[1] GAO Ya;WU Hong-bo(College of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710062,Shaanxi,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710062

出　　处：《山东大学学报（理学版）》2022年第4期30-36,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61572016,11531009,61673250)。

摘　　要：由于拓扑系统中闭元的缺失,对拓扑系统中与闭集相关内容的理论及性质研究受到一定程度的制约。首先利用余frame和点集两部分建立对偶拓扑系统——由闭元确定的拓扑系统,对其基本性质进行初步讨论;其次利用闭元给出点集部分的闭包元概念,并对闭包元性质进行讨论;第三,利用闭包元给出拓扑系统中凝聚点和导集的定义,对导集和闭包集的性质进行讨论。最后总结讨论闭包元和闭包集的关系。Because of the lack of closed elements in topological systems,the research on the theory and properties of closed sets in topological systems is restricted to a certain extent.In this paper,the dual topological system,the topological system determined by closed elements,is established by using the coframe and the point set,and its basic properties are discussed.Secondly,the concept of closure element of point set part is given by using closed element,and the properties of closure element are discussed.Thirdly,the definition of condensation point and derived set in topological system is given by using closure element,and the properties of derived set and closure set are discussed.Finally,the relationship between closure element and closure set is discussed.

关 键 词：余frame 拓扑系统 闭包元 凝聚点 导集 闭包集 

分 类 号：O189.1[理学—数学] O153.1[理学—基础数学]