闭元确定的拓扑系统中闭包元及其应用  

Closure Elements in the Topological System Determined by Closed Elements with Applications

作　　者：高雅[1] 吴洪博[1] GAO Ya;WU Hong-bo(College of Mathematics and Statistics,Shaanxi Normal University,Xi'an,Shaanxi 710062,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：《电子学报》2022年第5期1270-1276,共7页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61572016,No.11531009,No.61673250)。

摘　　要：本文利用余Frame和点集两部分建立由闭元确定的拓扑系统,对其基本性质进行了讨论;通过闭元给出了点集部分的闭包元概念,并对闭包元性质进行了讨论.在余Frame和点集部分之间利用双映射建立了闭包元算子,证明了与拓扑系统相关的Kuratovski闭包定理;作为应用,利用闭包元算子对闭元确定的拓扑系统之间的连续映射进行了等价刻画.A topological system determined by closed elements is established with coframe and point set,and its basic properties are discussed.The concept of closure element of point set part is given through closed element,and the properties of closure element are discussed.The closed element operator is established through double mapping between coframe and point set,and the Kuratovski closure theorem related to topological system is proved.As an application,the continuous mapping between topological systems determined by closed elements is characterized by closure element operators.

关 键 词：拓扑系统 余Frame 闭元 闭包元 闭包算子 Kuratovski闭包定理 连续映射 

分 类 号：O189.1[理学—数学] O153.1[理学—基础数学] O141.1