σ-亚紧和σ-meso紧空间的σ-积

σ-PRODUCTS ON σ-METACOMPACT SPACES AND σ-MESOCOMPACT SPACES

主要获得如下两个结果 :(1)设Χ =σ{Χα∶α∈A} ,如果X的每个有限子积是σ 亚紧的 ,则Χ是σ 亚紧的 ;(2 )设X =σ{Xα∶α∈A} ,如果X的每个有限子积是σ meso紧 (σ 序列meso紧 )的且Χ正规 ,则Χ是σ meso紧 (σ 序列meso紧 )

It was mainly obtained that the following two results:(1)Let X=σ｛X α∶α∈A ｝,If every finite subproduct of X is σ metacompact,then X is σ metacompact;(2)Let X=σ｛X α∶α∈A} ,if every finite subproduct of X is σ mesocompact and X normal,then X is σ mesocompact.