完全基-仿紧空间的一些性质

Some Properties of Perfectly Base-paracompact Spaces

引入了完全基-仿紧空间,并且获得了如下主要结果:(1)设f:X→Y为完备映射,Y为完全基-仿紧空间,则X是完全基-仿紧空间;(2)设X是完全基-仿紧空间,Y是紧空间,则X×Y是完全基-仿紧空间;(3)设X是完全基-仿紧空间,Y是局部紧的完全基-仿紧空间,则X×Y是基-仿紧空间。

The notion of perfectly base-paracompact spaces is introduced and the following results are proved. （1） Let f： Z→Y be a perfect mapping, if Y is a perfectly base-paracompact space, then X is perfectly base-paracompact;（2）Let X is a perfectly base-paracompact. If Y is compact, then X×Y is perfectly base-paracompact;（3） Let Z is perfectly base-paracompact, if Y is locally com-pact,then X×Y is base-paracompact.