| 引用本文： |
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陈海燕,王培,刘士琴,郑顶伟.ℵ0-弱基及相关问题[J].广西科学,2007,14(4):354-356. [点击复制]
- CHEN Hai-yan,WANG Pei,LIU Shi-qin,ZHENG Ding-wei.ℵ0-Weak Base and Related Matters[J].Guangxi Sciences,2007,14(4):354-356. [点击复制]
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| 摘要: |
| 证明在空间X中下列论述等价:(1)X有σ-离散的ℵ0-弱基;(2)X有σ-局部有限的ℵ0-弱基;(3)X是ℵ0-弱第一可数的空间,ℵ0-弱基是开、闭遗传的,点可数ℵ0-弱基是cs*-网.并讨论ℵ0-弱基,sn-网,cs-网以及cs*-网的关系. |
| 关键词: ℵ0-弱基 ℵ-空间 sn-度量空间 sn-第一可数 cs*-网 cs-网 |
| DOI： |
| 投稿时间：2007-06-21修订日期：2007-07-25 |
| 基金项目:Supported by the Natural Science Foundation of Guangxi (No0728035). |
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| ℵ0-Weak Base and Related Matters |
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CHEN Hai-yan, WANG Pei, LIU Shi-qin, ZHENG Ding-wei
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| (College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| It is proved that the followings are equivalent for a space X: (1) X has a σ-discrete ℵ0-weak base; (2)X has a σ-locally finite ℵ0-weak base; (3)X is a ℵ0-weakly first-countable and ℵ-space, space with ℵ0-weak base is open, closed hereditary, and point-countable ℵ0-weak base is cs*-network.Some relations are discussed among ℵ0-weak base, sn-network, cs-network and cs*-network. |
| Key words: ℵ0-weak base ℵ-space sn-metric space sn-first countable cs*-network cs-network |
