关于正规可数中紧空间在逆极限运算下的保持问题

On Normal Countable Mesocompact Preserving Problem through the Operation of Inverse Limits

设X是逆系统{Xα,παβ,Λ}的逆极限,|Λ|=λ,假设每个投射πα:X→Xα是开且到上的,X是λ-仿紧的,如果每个Xα是正规可数中紧的,则X是正规可数中紧的.进一步,还得到了关于遗传性质的类似结果.

Let X be the limit of an inverse system {Xα,πα^β,∧}and λ is the cardinal number of ｜ ∧｜. Suppose each projection ∏α ：X → Xα is an open and onto map and X is λ- paracompact. If each Xα is a normal countable mesocompact space, then X is a countable mesocompact space. Moreover, the analogous result for hereditanily countable mesoompact properties is obtained. Key words： inverse limits; countably mesocompact; hereditarily countable mesocompact; λ- paracompact