关于Meso-紧在逆极限运算下的保持问题

On Mesocompactpreserving Problem Through the Operation of Inverse Limits

令Ｘ是逆系统｛Ｘσ，πσρ，Σ｝的逆极限，λ是Σ的基数，假设每一个投射πσ：Ｘ→Ｘσ是开且到上的，且Ｘ是λ仿紧的，如果每个Ｘσ是Ｍｅｓｏ紧的，则Ｘ是Ｍｅｓｏ紧的．进一步有遗传Ｍｅｓｏ紧的类似结果．

Let X be the inverse limit of an inverse system {Xσ,πσρ,Σ} and λ is cardinal number of Σ. Suppose each projection πσ:X→Xσ is an open and onto map and X is λ paracompact. If each Xσ is mesocompact, then X is mesocompact. Moreover, there are the analogous results for hereditarily mesocompact.