正规可数仿紧空间的逆极限

The Inverse Limits of Normal Countably Paracompact Spaces

得到了如下结果:设X是逆系统{Xα,παβ,Λ}的逆极限,|Λ|=λ,假设每个映射πα∶X→Xα是开的且到上的,X是λ-仿紧,每个Xα是正规可数仿紧的,则X是正规可数仿紧的.进一步得到了关于遗传正规且遗传可数仿紧空间的类似结果.

We prove the following： Let X be the limit of an inverse system {Xα,παβ,Λ} and λ the cardinal number of Λ.Suppose each projection πα：X→Xα is an open and onto map and X is λ-paracompact.If each Xα is a normal countably paracompact space,then X is a countably paracompact space.Moreover,we obtain the analogous result for hereditanily countably paracompact properties.