摘要
首先给出集体次正规空间的一组等价刻画.利用该组刻画证明:设X=lim{Xσ,πρσ,∑}并且每个投影映射πσ:X→Xσ是开满映射, (1)如果X是|∑|-仿紧的且每个Xσ是集体次正规空间,则X是正规集体次正规空间; (2)如果X是遗传|∑|-仿紧的且每个Xσ是遗传集体次正规空间,则X是遗传集体次正规空间.然后,在X=Ⅱα∈AXα是|A|-仿紧的条件下得到结果:X是集体次正规的当且仅当(?)F∈[A]<ω,Ⅱσ∈FXσ是集体次正规的,并且遗传集体次正规也有类似性质.
We first show that a group of the characterizations of collectionwise subnormal spaces. By using this, the following are proved: (1) Let X = lim{Xσ,πρσ, ∑} and every πσ be open and onto mapping, if X is |∑|-paracompact and every Xσ is collectionwise subnormal, then X is collectionwise subnormal; (2) Let X = ⅡαεXα be |A|-paracompact, X is collectionwise subnormal iff ⅡαεFXα is collectionwise subnormal for every F ε[A]<ω. Next, we point out that there exist the similar results to hereditarily collectionwise subnormal spaces.
出处
《数学进展》
CSCD
北大核心
2005年第1期80-84,共5页
Advances in Mathematics（China）
基金
四川省自然科学基金(No99LA47)
关键词
逆极限
|∑|-仿紧
集体次正规
遗传集体次正规
inverse limit
|∑|-paracompact
collectionwise subnormal
hereditarily cokkectionwise subnormal
