几乎仿紧空间  

Nearly paracompact spaces

作　　者：曹金文[1] 

机构地区：[1]成都理工大学应用数学系,四川成都610056

出　　处：《纯粹数学与应用数学》2003年第1期57-61,共5页Pure and Applied Mathematics

摘　　要：主要证明了如下结果 :( 1 )如果 X =∏α∈ΛXα是 |Λ | -仿紧空间 ,则 X是几乎仿紧 (仿 - L indelof)空间当且仅当 F∈ [Λ ]<ω,∏α∈ FXα是几乎仿紧 (仿 - L indelof)空间 .( 2 )如果 X =∏i∈ωXi 是可数仿紧的 ,则下列三条等价 :X是几乎仿紧 (仿 - L indelof)的 : F∈ [ω]<ω,∏i∈ FXi是几乎仿紧 (仿 - L indelof)的 : n∈ω,∏i≤ nXi是几乎仿紧 (仿- Lindelof)的 .最后还给出了几乎仿紧 (仿 - L indelof)This paper mainly proves following: (1) Let X=∏α∈ΛX α be |Λ|- paracompact, X is nearly paracompact (para-Lindelof)iff ∏α∈FX α is nearly paracompact (para-Lindelof) for every F∈ <ω.(2) Let X=∏i∈ωX i is countable paracompact,then the following are equivalent: X is nearly paracompact (para-Lindelof) for every F∈ <ω;F∈ <ω,∏i∈FX i is nearly paracompact (para-Lindelof);n∈ω, ∏i≤nX i is nearly paracompact (para-Lindelof).Finally, the equalent propositions on nearly paracompact (para-Lindelof) and the equalent propositions on paracompact (para-Lindelof) are obtained.

关 键 词：几乎仿紧(仿-Lindelof) |∧|-仿紧 可数仿紧 

分 类 号：O189.11[理学—数学]