σ-正紧空间的逆极限

The Inverse Limit on σ-Orthocompact Space

本文主要得到如下结果: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,如果每一个Xα是σ-正紧的,则X是σ-正紧的,进一步还得到有遗传-σ正紧的类似结果。

The following is proved： Let X be the inverse limit of an inverse system {Xα,πβ^α,Λ} and λ the cardinal number of A. Suppose each projetions πα： X→Xα is an open and onto map and X is λ-paracompact. If each Xα is σ-Orthoeompect, then X is σ-Orthoeompect. Moreover, the analogous results for hereditarily σ-Orthoeompaet are obtained.