摘要
证明了:几乎中紧空间的闭子集是几乎中紧的;空间X是几乎中紧的当且仅当X的一单调开覆盖U,■X的稠密子集D和U的一开加细U',使得D中一紧集K,有(U')K是有限集;如果X=∏α∈ΛX_α是|Λ|-仿紧空间,则X是几乎中紧空间F∈[Λ]ω,∏α∈ΛX_α是几乎中紧的;几乎中紧空间X,如果是T3空间且是可数紧空间,那么它也是紧空间.
This paper mainly proves the following points:( 1) Every closed subspace of nearly mesocompact spaces is nearly mesocompact.( 2) A space X is nearly mesocompact if and only if every monotone open cover U has an open refinement that is compact-finite on some dense subset of X.( 3)Let X = ∏α∈ΛX_αbe a | Λ |-paracompact space,then X is nearly mesocompact space if and only if ∏α∈ΛXαis nearly mesocompact for each F∈[Λ]ω.( 4) nearly mesocompact spaces X,if T_3-space is nearly mesocompact space,X is also mesocompact space.
出处
《成都大学学报(自然科学版)》
2016年第2期140-142,共3页
Journal of Chengdu University(Natural Science Edition)
关键词
闭子空间
几乎中紧空间
|Λ|-仿紧空间
紧有限
closed subspace
nearly mesocompact spaces
| Λ |-paracompact space
compact-finite