DCCC与*Lindelf性之间的两种覆盖性质

Two Covering Properties between DCCC and *Lindelfness

本文证明了关于拓朴空间度量化的两个结论:(1)局部 CCC 正则空间当它具有σ互斥基或者σ局部可数基时,是可度量的;(2)全、正则、局部点有限 Lindelf 空间当它具有σ点限基或σ局部可数基时,是可度量的。文中也给出了两个可数紧空间其乘积包含有势为 k(ω<K<2ω)的离散开集族的例子。

Two results on metrization of topological spaces are proved. (1) A locally CCC regular space with a σ-disjoint base or a σ-locally countable bass is metrizable.(2) A perfect,regular,locally pointfinite Lindelf space with a σ-pointfinite base or a σ-locally countable base is metrizable.The example that the product of two countably compact spaces has a discrete collection of open sets which hascardinality κ,ω<κ≤2~ω,is given too.