| 一致覆盖和度量空间的紧映象 |
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| 引用本文： | 葛英,林寿.一致覆盖和度量空间的紧映象[J].数学学报,2004,47(6):1149-115. |
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| 作者姓名： | 葛英 林寿 |
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| 作者单位： | 1. 苏州大学数学系,苏州,215006
2. 宁德师范高等专科学校数学系,宁德,352100 |
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| 基金项目： | 国家自然科学基金(10271026)，江苏省教育厅自然科学基金(02KJB110001)，福建省自然科学基金(F0310010) |
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| 摘 要： | 本文利用一致覆盖的概念,讨论了度量空间的序列覆盖紧映象的结构.主要结果有: (1)空间X是局部可分度量空间的序列覆盖紧映象当且仅当X具有由cosmic子空间构成的一致sn网; (2)空间X是局部可分度量空间的序列覆盖,商紧映象当且仅当X是度量空间的序列覆盖,商紧映象且是局部cosmic空间.
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| 关 键 词： | 序列覆盖映射 一致覆盖 点星网 |
| 文章编号： | 0583-1431(2004)06-1149-06 |
Uniform Covers and Compact Images of Metric Spaces |
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| Ying GE.Uniform Covers and Compact Images of Metric Spaces[J].Acta Mathematica Sinica,2004,47(6):1149-115. |
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| Authors: | Ying GE |
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| Institution: | Ying GE (Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China) Shou LIN (Department of Mathematics, Ningde Teachers' College, Ningde 352100, P. R. China) |
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| Abstract: | In this paper the structures of sequence-covering compact images of locally separable metric spaces are investigated by uniform covers, the main results are that (1) a space is a sequence-covering compact image of a locally separable metric space if and only if it has a uniform sn-network consisting of cosmic subspaces; (2) a space is a sequence-covering quotient compact image of a locally separable metric space if and only if it is a locally cosmic space and a sequence-covering quotient compact image of a metric space. |
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| Keywords: | Sequence-covering mappings Uniform covers Point-star networks |
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