S-可数仿紧空间  

S-countably Paracompact Spaces

作　　者：孙文 何兆容 SUN Wen;HE Zhaorong(No.3 High School in Panzhihua,Panzhihua 617000,China;College of Science,Shantou University,Shantou 515063,China)

机构地区：[1]四川省攀枝花市第三高级中学,四川攀枝花617000 [2]汕头大学理学院,广东汕头515063

出　　处：《安庆师范大学学报（自然科学版）》2018年第2期6-9,共4页Journal of Anqing Normal University(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S-仿紧空间和可数仿紧空间的概念和性质,引入了S-可数仿紧空间,并在拓扑空间中基于广义仿紧空间和半开集的诸多性质研究了S-仿紧空间的等价刻画、覆盖性质、正规性、映射性质和乘积性质,并得出S-可数仿紧空间在准完备映射下的原像是S-可数仿紧空间、S-可数仿紧空间与紧空间的乘积是S-可数仿紧空间、半正规S-可数仿紧空间与紧度量空间的乘积是半正规空间等结果。Combining the conceptions and the properties of S-paracompact spaces with countably paracompact spaces,the new topological conception S-countably paracompact spaces are introduced. Based on the characteristics and properties of generalized paracompact spaces and semi-open sets in topology, some equivalent characteristics, semi-normality, mapping properties and finite product of S-countably paracompact spaces are instigated, and several main results are obtain. Such as the inverse of a S-countably paracompact space under a quasi-perfect mapping is also S-countably paracompact, the product of a S-countably paracompact space and a compact space is S-countably paracompact, the product of a semi-normal S-countably paracompact space and a compact metric space is semi-normal.

关 键 词：S-可数仿紧 半开集 半正规空间 乘积 

分 类 号：O189[理学—数学]