几乎中紧空间

Nearly Mesocompact Spaces

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.