遗传σ-meso紧空间  

Hereditarily σ-Mesocompact Spaces

作　　者：曹金文[1] 贾永进[1] 杨建康[1] 

机构地区：[1]成都理工大学应用数学系,四川成都610059

出　　处：《江西师范大学学报（自然科学版）》2007年第1期17-20,共4页Journal of Jiangxi Normal University(Natural Science Edition)

摘　　要：获得了如下结果:(1)对任何空间X,下列各条等价:(ⅰ)X是遗传σ-meso紧的;(ⅱ)X的每个散射分解有一个σ-紧有限的开膨胀;(ⅲ)X的每个单调递减的闭集族{Fα:α<γ}有一个σ-紧有限的开集族V=∪n∈ωVn使得α<γ,X-Fα=∪{V∈V:V∩Fα=Φ};(ⅳ)X的每个单调递增的开集族U={Uα:α<γ}有一个σ-紧有限的开加细V=∪n∈ωVn使得α<γ,Uα=∪{V∈V:VUα};(ⅴ)X的每个单调递增的开覆盖U={Uα:α<γ}有一个σ-紧有限的开加细V=∪n∈ωVn使得α<γ,Uα=∪{V∈V:VUα}.(2)设X是遗传σ-meso紧空间且Y有一个σ-紧有限的基,则X×Y是遗传σ-meso紧的.In this paper we shall prove the following result： （1）For every space X,the followings are equivalent： （ⅰ）X is hereditarily σ-mesocompact; （ⅱ）Every scattered partition of X has a σ-compact finite open expansion; （ⅲ）Every monotone decreasing family {Fα：α〈γ} of close sets of X has a σ-compact finite open family V=∪n∈ωVn such that,for every α〈γ,X-Fα=∪{V∈V：V∩Fα=Φ}; （ⅳ）Every monotone increasing family U={Uα：α〈γ} of open sets of X has a σ-compact finite open refinement V=∪n∈ωVn such that,for every α〈γ,Uα=∪{V∈V：V blong to Uα}; （ V ） Every monotone increasing family U={Uα：α〈γ} of open cover of X has a σ-compact finite open refinement V= Un∈ω Vn nsuch that, for every α〈γ,Uα= U { V∈V：V belong to Uα}; （2）If X is hereditarily σ-meso compact space and Y has a bace of σ-compact finite , then X × Y is hereditarily σ-mesocompact space.

关 键 词：遗传σ-meso紧 散射分解 σ-紧有限的开膨胀 

分 类 号：O189.11[理学—数学]