摘要
证明了如下结果:(1)空间X是几乎次亚紧的当且仅当X是几乎离散次亚可膨胀的,并且X的每个开覆盖υ={Ua:a∈∧),都存在X的稠密子集D和υ的开加细序列<°νn>n∈ω,使得对于(?)∈D,存在n∈ω和a∈∧有x∈Ua,并且St(x,vn)(?)∪β≤α;(2)如果X=∏a∈A是|∧|-仿紧空间,则X是几乎次亚紧空间当且仅当(?)F∈|∧|<ω,∏Xi是几乎亚紧空间;(3)如果X=∏i∈ωXi是可数仿紧的,则下列三条等价:X是几乎次亚紧的;(?)F∈|ω|<ω,∏i∈FXi是几乎次亚紧的:(?)n∈ω,∏i≤nXi是几乎次亚紧的。
The following are proved: (1). A space X is nearly submetacompact if X is nearly discretely submetaexpandable and for every open over of X there is a dense set DX and a sequence of open refinements of u such that for each x∈D there are n∈w and a = A with
and St paracompact, X is nearly submetacompact iff
nearly submetacompact for every be countable paracompact, then the follow-
ing are equivalent: X is nearly submetacompact for every is nearly submet-acompact;
出处
《黑龙江大学自然科学学报》
CAS
2003年第3期50-53,共4页
Journal of Natural Science of Heilongjiang University
关键词
几乎次亚紧
几乎离散次亚可膨胀
|∧|-仿紧
可数仿紧
nearly submetacompact
nearly discretely submetaexpandable
|∧|-paracompact
countable paracompact
