基-亚紧和几乎亚紧空间的若干性质

Some Properties of Base-metacompact and Nearly Metacompact Spaces

文章着重证明了:(1)设X是亚紧空间,X=∪i<ωFi,Fi为相对X的基-亚紧闭子集,则X是基-亚紧的;(2)X是基-亚紧空间,若MX是Fσ集,且ω(M)=ω(X),则M为基-亚紧空间;(3)空间X是几乎亚紧的当且仅当X的每一单调开覆盖U有一个开加细,且在X的某一稠密子集上是点有限的;(4)可数紧的且为几乎亚紧的T3-空间是紧的。

In this paper, it is proved emphasizely that： （1） If X is metacompact and the countable union of closed base-metacompact sets relative to X ,then X is base-metacompact; （2） Let X be base-metacompact .If M beloy to X is an Fσ set with ω（M）= ω（X）, then X is base-metacompact; （3） A space X is nearly metacompact if and only if every monotone open cover U has an open refinement that is point-finite on some dense subset of X ; （4） A countable compact, nearly metacompact T3-space is compact.