S-弱θ-Lindelff加细空间  

S-weak θ-Lindelff-refinable spaces

作　　者：孙文[1,2] 何兆容 SUN Wen;HE Zhao-rong(College of Management Science,Chengdu University of Technology,Chengdu 610059,China;No.3 High School in Panzhihua,Sichuan Province,Panzhihua 617000,China;College of Science,Shantou University,Shantou 515063,China)

机构地区：[1]成都理工大学管理科学学院,四川成都610059 [2]四川省攀枝花市第三高级中学,四川攀枝花617000 [3]汕头大学理学院,广东汕头515063

出　　处：《山东理工大学学报（自然科学版）》2018年第3期17-20,共4页Journal of Shandong University of Technology:Natural Science Edition

基　　金：安徽省高等学校省级优秀青年人才基金项目(2010SQRL158)

摘　　要：结合弱θ-加细空间、θ-加细空间、Lindelff空间以及S-仿紧空间的概念和有关性质,新引入了S-弱θ-Lindelff加细空间和S-θ-Lindelff加细空间.然后在拓扑空间中半开集上研究了S-弱θ-Lindelff加细空间和S-θ-Lindelff加细空间的刻画性质、完备性、映射性质以及两者之间的关系,并得出几个主要结果.如完备的S-弱θ-Lindelff加细空间是S-次仿紧空间;S-弱θ-Lindelff加细空间在闭Lindelff映射下的像是S-弱θ-Lindelff加细空间等.Combiningθ-refinable spaces with weakθ-refinable spaces,comparing LindelOff spaces with S-paracompact spaces,and studying the conceptions and related properties of them,the new types of spaces are introduced.Namely S-weakθ-LindelOff refinable spaces and S-θ-LindelOff refinable spaces.Based on the conceptions of semi-open set and semi-closed set in topological space,the characteristics and properties of S-weak-LindelOff and S-θ-LindelOff refinable spaces are investigated,then several main results are obtained.Complete S-weak-LindelOff refinable spaces are S-subparacompact spaces.The closed LindelOff mapping of S-weakθ-LindelOff refinable space is also refinable.

关 键 词：S-弱θ-LindelOff加细 S-θ-LindelOff加细 半开集 完备空间 闭LindelOff映射 

分 类 号：O189[理学—数学]