几乎可数仿紧空间的性质与刻画  

Properties and Characterization of Nearly Countable Paracompact Spaces

作　　者：蔡奇嵘[1] 刘唐伟[1] 

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《东华理工大学学报（自然科学版）》2015年第4期458-460,共3页Journal of East China University of Technology(Natural Science)

基　　金：江西省自然科学基金资助项目(20114BAB201016);江西省教改基金资助项目(JXJG-11-8-21)

摘　　要：在Elise Grabner定义几乎亚紧空间的基础上,引入了几乎可数仿紧空间,得到了一个关于它的等价刻画定理:X为几乎可数仿紧空间当且仅当X的每个可数散射分解有一个几乎局部有限的开膨胀。讨论了几乎仿紧空间、几乎可膨胀空间、几乎可数仿紧空间三者之间的关系:几乎κ-仿紧空间是几乎κ-可膨胀的。空间X是几乎可数仿紧的当且仅当X是几乎可数可膨胀的。The notion of nearly countable paracompaet spaces on the basis of Elise Grabner defined nearly meta- compact spaces are introduced, get a equivalent charaeterization ：X is a nearly countable paracompact space if and only if every scattered partition of X have a nearly locally finite open expansion. And also discuss of the relation- ship between nearly κ-paracompaet spaces, nearly countable paraeompact spaces and nearly κ-expandable spaces： Nearly κ-paracompact space is a Nearly κ-expandable space. X is a nearly countable paracompact space if and on- ly if X is a nearly countable expandable snack.

关 键 词：几乎可数仿紧 几乎可膨胀 几乎局部有限 散射分解 

分 类 号：O189.11[理学—数学]