| 引用本文： |
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刘川,宣泽永,谷建胜.关于σ-局部可数基[J].广西科学,1994,1(2):5-6,11. [点击复制]
- Liu Chuan,Xuan Zeyong,Gu Jiansheng.On σ-locally Countable Bases[J].Guangxi Sciences,1994,1(2):5-6,11. [点击复制]
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| 摘要: |
| 证明了下列两个定理:(1)X有σ-局部可数基的充分必要条件是X是q-空间且有-σ-局部可数k-网.(2)设Xn(n∈N)具有σ-局部k-网,若Πi∈N为k-空间,则下列之一成立.①每一Xi有σ-局部可数基.②除有限多个Xi外.Xi(i∈N)为紧可度量空间. |
| 关键词: 基 k-网 q-空间 完全映射 σ-局部可数 |
| DOI： |
| 投稿时间：1993-09-11 |
| 基金项目:国家自然科学基金和广西区教委基金 |
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| On σ-locally Countable Bases |
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Liu Chuan1, Xuan Zeyong1, Gu Jiansheng2
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| (1.Dept. of Math. & Inf's Sci. Guangxi University, 10 Xixiangtang Road, Nanning, Guangxi, 530004;2.Dept. of Math., Suzhou Railway Teacher's College, Hetang, Suzhou, Jiangsu, 215009) |
| Abstract: |
| Two main theorems are proved:(1) Topological space X has a σ-locally countable base if X is a q-space with a σ-locally countable k-network;(2) Let Xn (n∈N) have a σ-locally countable k-network.If Πi∈N X is a k-space, then one of the following holds:①Each Xi has a σ-locally countable base; ②All but finitely many Xi,Xi(i∈N) are compact metrizable spaces. |
| Key words: base k-netword q-space perfect mappings σ-locally countable |
