几乎可数仿紧空间的性质与刻画

Properties and Characterization of Nearly Countable Paracompact Spaces

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.