σ-MESO-紧空间的逆极限

The inverse limit of σmesocompact space

得到了如下结果：设Ｘ是逆系统｛Ｘａ，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σＭｅｓｏ紧的，则Ｘ是σＭｅｓｏ紧的．进一步。

he following is proved: Let X be the inverse limit of an inverse system {Xα, παβ, Λ} and λ the cardinal number of Λ. Suppose each projection πα: XX α is an open and onto map and X is λparacompact. If each X α is σMesocompact, then X is σMesocompact. Moreover, the analogous results for hereditarily σMesocampact are obtained. 