遗传σ-ortho紧空间的刻画  

On some characterizations of hereditary σ-orthospact spaces

作　　者：曹金文[1] 李焱[1] 吴惠[1] 

机构地区：[1]成都理工大学信息管理学院,成都610059

出　　处：《成都理工大学学报（自然科学版）》2009年第1期94-97,共4页Journal of Chengdu University of Technology: Science & Technology Edition

基　　金：四川省教育厅科研基金(2006C041);成都理工大学科学基金资助项目(R230246)

摘　　要：回答了关于σ-ortho紧空间遗传性的一个问题,获得了遗传σ-ortho紧空间的等价刻画。主要结论有:X是遗传σ-ortho紧空间当且仅当X的每一个散射分解有一个σ内部保持的开膨胀;设X是拓扑空间,则下列条件等价:(1)X是遗传σ-ortho紧空间;(2)X的每个单调递减的闭集族{Fα:α<γ}有一个σ内部保持的开集族V=∪n∈ωVn使得α<γ,X-Fα=∪{V∈V:V∩Fα=};(3)X的每个单调递增的开集族U={Uα:α<γ}有一个σ内部保持的开加细V=∪n∈ωVn使得α<γ,Uα=∪{V∈V:V Uα}。This paper answers a problem about the heredity of a-orthospact space and deduces that there are two groups of equivalent characterizations for all such X from this result. The main results is that a space X is hereditary σ-orthospact space if and only if every scattered partition of X is a σ- interior preserving of open expansions. Let X be a topological space,then the following conditions are equivalent： （1） X is hereditary a-orthospact space; （2） Every monotone decreasing family{Fα：α〈γ} of close sets of X has a σ- interior preserving open family ∨=Un∈ωνn such that, for every α〈γ , X--Fα =U{V∈∨：∨∩Fα=φ} ; （3） Every monotone increasing family u={Uα：α〈γ} of open sets of X has a σ- interior preserving open refinement ∨=Un∈ωVn such that,for every α〈γ,Uα={∨∈V：V∨ belong to ∪α}.

关 键 词：遗传σ-ortho紧 散射分解 σ内部保持开膨胀 

分 类 号：O189.11[理学—数学]