S-次仿紧空间  

S-subparacompact Spaces

作　　者：何兆容 石鹏飞[1] 孙文[1] 

机构地区：[1]成都理工大学管理科学学院,四川成都610059

出　　处：《佳木斯大学学报（自然科学版）》2014年第6期947-949,共3页Journal of Jiamusi 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：针对一些广义仿紧空间以及拓扑空间中半开集和半闭集的性质,本文将次仿紧空间的一些结论推广到半闭集的条件下,新定义并研究S-次仿紧空间的基本性质.首先给出一些基本的定义和定理,然后在此基础上定义S-次仿紧空间,最后得出一些主要结果:(1)空间X是S-次仿紧空间,则X的每一开覆盖U,存在半开加细覆盖序列{Vn}n∈N使对每一x∈X,存在n∈N,使ord(x,Vn)=1,这里(ord(x,Vn)=|{V:V∈Vn,x∈V}|);(2)空间X是S-次仿紧空间,则X的每一开覆盖具有σ垫状加细覆盖;(3)如果(X,Fa)是S-次仿紧空间,则(X,F)也是S-次仿紧空间,并给出相应的证明.Based on a series of generalized paracompact spaces and the properties of semi -open and semi-closed sets in topological spaces , some conclusions of sub -paracompact spaces were spread to semi -closed sets.The definition of S -subparacomact space was given and its basic properties was studied .Some basic defi-nitions and theorems in topological spaces were given first , and then the definition of S -subparacompact space was introduced .Some main results were obtained as follows： （ 1 ） Let X be a S-subparacompact space , then each open cover U of X has a semi-open n∈N refinements{Vn}n∈N and for every x∈X , there exists a positive integrity such that only belongs to one set of Vn ,i.e.ord（ x,Vn ） =1 .（2） If X is a S-subparacompact space . Then each open cover U of X has a refinement which isσ-cushioned in the family U .（3） Suppose （X,Tα） is a S-subparacompact space.Then the space （X,T） is S-subparacompact.At same time, their corresponding proofs are presented .

关 键 词：S-次仿紧 S-仿紧 半开覆盖 半闭覆盖 垫状 

分 类 号：O189[理学—数学]