基-可数仿紧空间的刻画  

Some Characterizations of Base-countably Paracompact Spaces

作　　者：付传秀[1] 周建新[1] 

机构地区：[1]成都理工大学信息管理学院,四川成都610059

出　　处：《湖北民族学院学报（自然科学版）》2007年第3期263-265,共3页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：安徽省教育厅自然科学基金资助项目(KJ2007B123)

摘　　要：引入了基-可数仿紧空间的概念,给出基-可数仿紧空间的一些等价刻画,获得以下结果:(i)X是基-可数仿紧空间当且仅当存在X的一开基B,|B|=ω(X),对于X的每一可数开覆盖U={Ui}i∈N,都存在B′B,使得B′={Bi}i∈N是U的局部有限的可数开加细,且BiUi;(ii)设X是正规空间,X是基-可数仿紧空间当且仅当存在的一开基B,|B|=ω(X),使得X的每一可数开覆盖都存在由B中的元构成的局部有限的收缩.The notion of base - countably paracompact space is introduced and some of its equivalent characterizations are obtained：（i） X is a base -countably paracompact space if there exsists an open basis B for X with ｜B｜ = ω（X） such that every countably open cover U = { Ui }i∈N of X has a locally finite countabe refinement B′ by mem- bers of B,B′ = { Bi} i∈N and Bi beling to U.. （ii） Let X is normal ,X is a base - countably paracompact space if there exsists an open basis B for X with ｜B｜ = ω （X） such that every countably open cover of X has a locally finite shrinking by members of the basis B.

关 键 词：基 基-仿紧空间 基-可数仿紧空间 局部有限 

分 类 号：O189.1[理学—数学]