■_0-sn-网的注记

A note on ■_0-sn-network

利用序列商映射建立了具有可数■0-sn-网的空间与可分度量空间之间的联系,讨论了可分度量空间的可数到一、序列商映像。证明了在序列空间中,下列叙述等价:(1)X有σ-离散的■0-sn-网;(2)X有σ-局部有限的■0-sn-网;(3)X有σ-遗传闭包保持的■0-sn-网;(4)X是■0-sn-弱第一可数的■-空间;(5)X有由闭子集构成的σ-紧有限的■0-sn-网。

The relations between a space with countable R0-sn-network and separable metric spaces are established by means of sequentially quotient map, and separable metric space is discussed by sequentially quotient and countable-to-one maps. The following are equivalent and proved for a sequence space X： （ 1 ） X has ao--discrete Ro-sn-network, （2） X has a o--locally finite N0-sn-network, （3） X has a tr-hereditadly closure-preserving N0-sn-network, （4） X is an Ro-sn- weakly first-countable and R-space, and （5） X has an tr-compact-finitei, N0-sn-network consisting of closed subsets.