几乎弱加细空间

Nearly Weak  Refinable Spaces

证明了如下结果:(1)空间X是几乎弱加细空间当且仅当X是几乎离散弱加细可膨胀的,并且X的每个开覆盖u={Uα:α∈Λ},都存在X的稠密子集D和u的开加细V=∪n∈ωVn,使得x∈D存在b∈ω和α∈Λ有x∈Uα,并且st(x,Vn)∪βα;(2)如果X=∏α∈λXα是|Λ|—仿紧空间,则X是几乎弱加细空间,当且仅当F∈[Λ]<ω,∏α∈FXα是几乎弱加细空间;(3)如果X=∏α∈ΛXα是可数仿紧的,则下列三条等价:X是几乎弱加细空间;F∈[Λ]<ω,α∏∈FXα是几乎弱加细的;n∈ω,i∏nXi是几乎弱加细的。

The following results are proved （ 1 ） A space X is nearly weak ^-θ refinable iff X is nearly discrately weak ^-θ refinable expandable and for every open cover V= { Uα ：α ∈ ∧} of X then there is a dense set D belong to X and a V= Un∈ω Vn of open refinements of V such that for each x∈D there are n∈ω and α∈∧ with x∈Uα and st （ x,Vn） belong to U β≤α; （ 2 ） let X=П Xα be ｜∑｜- paracompact, then it is weak ^-θ refinable space if Пα∈F Xα is weak ^-θ refinable space for every F∈[ω]^〈ω;（ 3 ）and for countable paracompace X=Пα∈∧ Xi, the followings are equivalent ：X is weak ^-θrefinable ;arbitary F∈[ω]^〈ω,Пα∈F Xi is nearly weak ^-θrefinable ;arbitary n∈ω,Пi≤n Xi is weak ^-θrefinable space.