弱次-ortho-紧空间的σ-积

THE WEAKLY SUBORTHOCOMPACTNESS OF σ-PRODUCTS

本文研究了具有覆盖性质的弱次-ortho-紧空间的σ-积问题,证明存在可数仿紧空间族{X_α:α∈ω_1}满足:(1)空间σ{X_α:α∈ω_1}的每个有限子乘积是弱次-ortho-紧的;(2)空间σ{X_α:α∈ω_1}不是弱次-ortho-紧的.利用拓扑空间乘积性理论,获得了如下结果:设X=σ{X_α:α∈A}是|A|-仿紧空间.如果X的每个有限子乘积是弱次-ortho-紧的,则X也是弱次-ortho-紧的.从而推广了文献[8]的结果.

In this paper,we discuss the σ-products of weakly suborthocompact spaces characterized by covering.We present that there exists a collection of countably paracompact spaces {Xα：α∈ω1} such that：（1） Each finite subproduct of σ{Xα：α∈ω1} are weakly suborthocompact;（2） The space σ{Xα：α∈ω1} is not weakly suborthocompact.Finally,by using the products of topological spaces,we prove that if X=σ{Xα：α∈A} is a ｜A｜-paracompact space with every finite subproduct of X being weakly suborthocompact,then X is weakly suborthocompact,which generalizes the result in[8].