几乎基-亚紧空间

Nearly Base-metacompact Spaces

通过介绍几乎基-亚紧定义,研究了几乎基-亚紧空间,得到如下结论:(1)若X是可数个相对于X是几乎基-亚紧的闭集的并,则X是几乎基-亚紧的;(2)空间X是几乎基-亚紧的,当且仅当它有一个开基B,且|B|=ω(X),和一个稠密子集D■X,使得对X的每一个定向开覆盖在D上有一个点有限加细.

We introduce the notion of nearly base-metacompactness, mainly study nearly base- metacompactness of topological spaces. We prove the following： （ 1 ） If X is the countable union of closed nearly base-metacompaet sets relative to X, then X is nearly base-metacompact. （2） A space X is nearly base-metacompact if and only if it has an open base B with ｜B｜ = w（X） , and a dense set D X such that every directed open cover of X has a point-finite refinement by members of B on D .