| 关于序列覆盖紧映射 |
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| 引用本文： | 林寿,燕鹏飞.关于序列覆盖紧映射[J].数学学报,2001,44(1):175-182. |
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| 作者姓名： | 林寿 燕鹏飞 |
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| 作者单位： | 1. 福建师范大学数学系
2. 安徽大学数学系 |
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| 基金项目： | 国家自然科学基金(19501023，19971048);福建省自然科学基金及“百千万人才工程，，基金资助项目 |
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| 摘 要： | 本文利用了ｃｓ网、序列邻域网、序列开网和弱基的概念，讨论了空间中点正则覆盖，一致覆盖和点有限覆盖的点星网之间的关系．建立了度量空间在几类序列覆盖（紧）映射下象空间的特征，特别地证明了度量空间的序列覆盖（或１序列覆盖）紧映象等价于具有点正则ｃｓ网的空问，回答了Ｔａｎａｋａ等提出的一个问题．
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| 关 键 词： | 点正则覆盖 cs网 序列邻域网 序列覆盖映射 |
| 修稿时间： | 1999年2月1日 |
On Sequence-Covering Compact Mappings |
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| LIN Shou,YAN PengFei.On Sequence-Covering Compact Mappings[J].Acta Mathematica Sinica,2001,44(1):175-182. |
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| Authors: | LIN Shou YAN PengFei |
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| Institution: | LIN Shou (Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China) (Fax: (0593)2954127; E-mail: linshou@public.ndptt.fj.cn) YAN Peng Fei (Department of Mathematics, Anhui Univertsity, Hefei 230039, P. R. China) |
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| Abstract: | In this paper authors use the concepts of cs-networks, sequential-neighbor- hood networks, sequential-open networks and weak bases, discuss the relations among point-regular covers, uniform covers and point-star networks of point-finite covers in spaces, and establish the characterizations of images of metric spaces under some sequence-covering (compact) mappings. In particular, it is shown that the image of metric spaces under sequence-covering (or 1-sequence-covering) compact mappings is equivalent to the space with point-regular cs-networks, which answers a Tanaka's question. |
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| Keywords: | Point-regular cover cs-networks Sequential-neighborhood networks Se quence covering mappings |
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