正规σ-集体正规空间的逆极限

INVERSE LIMITS OF NORMAL σ COLLECTIONWISE NORMAL SPACES

本文得到如下结果：设Ｘ是逆系统｛Ｘα，παβ，Λ｝的极限，｜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σ－集体正规的，则Ｘ是集体正规的．进一步还要得到关于遗传σ－集体正规的类似结果．

Let X be the limit of an inverse system {X α, π α β ,Λ} and λ the cardinal number of Λ . Suppose each projection π α:X→X α is an open and onto map and X is λ paracompact. If each X α is normal σ collectionwise normal, then X is collectionwise normal. The analogous result for hereditarily σ collectionwise normal spaces is obtained.