关于弱aD-空间的有限并

On finite unions of weakly-aD spaces

研究了弱aD-空间的有限并,获得了如下结果:(1)如果X是亚紧空间,X=Y∪Z,其中Y是亚Lindelof空间,Z是弱aD-空间,则X是弱aD-空间;(2)如果X是亚紧空间,X=Y∪Z,其中Y是亚Lindelof空间,Z是弱aD-空间,则X是aD-空间,也是bD-空间;(3)如果亚紧空间X是亚Lindelof空间有限族{X i,i=1,,i}的并,则X是aD-空间,也是bD-空间。

In this paper,we study finite unions of weakly aD-spaces and get the following results：（1） If a metacompac X=Y∪Z,whereY is a metaLindelof space and Z is a weakly aD-space,then X is a weakly aD-spaces.（2）If metacompact X=Y∪Z,whereY is a metaLindelof space and Z is a weakly aD-spaces,then is X an aD -spaces,and it is also a bD-spaces.（3） If a metacompact X is the union of a finite collection {X i,i=1,,i}of metaLindelof spaces,then X is an aD-spaces,and it is also a bD-spaces.