■_0-弱基及相关问题(英文)

■_0-Weak Base and Related Matters

证明在空间X中下列论述等价:(1)X有σ-离散的■0-弱基;(2)X有σ-局部有限的■0-弱基;(3)X是■0-弱第一可数的空间,■0-弱基是开、闭遗传的,点可数■0-弱基是cs*-网.并讨论■0-弱基,sn-网,cs-网以及cs*-网的关系.

It is proved that the followings are equivalent for a space X ： （1） X has a a -discrete 0 - weak base; （2） X has a a-locally finite 0 -weak base; （3） X is a 0 -weakly first-countable and -space,space with 0 -weak base is open, closed hereditary,and point-countable 0-weak base is cs^＊-network. Some relations are discussed among 0 -weak base,sn-network,cs-network and cs^＊- network.