拓扑空间中的理想收敛  

Ideal Convergence in Topological Space

作　　者：王武[1] 张舜 WANG Wu;ZHANG Shun(Department of Foundation,Zhonghuan Information College Tianjin University of Technology,Tianjin 300380,China;Department of Mathematics Teaching,Tianjin Ren’ai College,Tianjin 301636,China)

机构地区：[1]天津理工大学中环信息学院基础部,天津300380 [2]天津仁爱学院数学教学部,天津301636

出　　处：《吉林大学学报（理学版）》2024年第1期13-19,共7页Journal of Jilin University:Science Edition

基　　金：天津市教委科研计划项目(批准号:2023KJ281);高等学校大学数学教学研究与发展中心教改项目(批准号:CMC20210115)。

摘　　要：用理想收敛结构解决定向拓扑的刻画问题,给出理想S极限和理想广义S极限可拓扑化的充要条件.结果表明:T0拓扑空间上的定向拓扑、理想S极限拓扑和理想广义S极限拓扑相同;定向空间中的理想S收敛是拓扑的当且仅当其为c-空间;定向空间中理想广义S收敛是拓扑的当且仅当其为局部强紧空间.We used an ideal convergence structure to solve the characterization problem of directed topology,and provided necessary and sufficient conditions for the topological transformation of ideal S limits and ideal generalized S limits.The results show that the directed topology,the ideal S limit topology and the ideal generalized S limit topology are the same in T 0 topological spaces.The ideal S convergence in a directed space is topological if and only if it is a c-space.The ideal generalized S convergence in a directed space is topological if and only if it is a locally strongly compact space.

关 键 词：理想S极限 理想广义S极限 c-空间 局部强紧空间 定向拓扑 

分 类 号：O153.1[理学—数学]