| 摘要: |
| 证明如下主要定理:(1)σ-局部可数弱基在开、闭Lindelöf映射下保持.(2)设X、Y有σ-局部可数弱基,则X×Y为k-空间的充分必要条件是下列之一满足:(a)X和Y有σ-局部可数基,(b)X或Y为局部紧度量空间,(C)X、Y有-σ-局部有限且由紧子集构成的弱基. |
| 关键词: 弱基 σ-局部可数 开映射 闭Lindelöf 映射 S2 |
| DOI： |
| 投稿时间：1995-03-27 |
| 基金项目:广西区教委基金 |
|
| On σ-locally Countable Weak Bases |
|
Xuan Zeyong1, Xiong Wen2
|
| (1.Dept. of Math. & Inf's Sci. Guangxi University Xixiangtang Road, Nanning, Guangxi, 530004;2.Traffic School of Guangxi, Yuanhu Road, Nanning, Guangxi, 530023) |
| Abstract: |
| Two main theorems are proved:(1) A σ-locally countable weak base is preserved under open and closed Lindelöf mappings. (2) Suppose that both X and Y have a σ-locally countable weak base then X×Y is a k-space if the following holds:①Both X and Y have a σ-locally countable base.② X or Y is a locally compact and metrizable space. ③ Both X and Y have a σ-locally countable weak base formed by compact subsets. |
| Key words: weak base σ-locally countable open maps closed Lindelöf maps S2 |
