| 连通度量空间的映象 |
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| 引用本文： | 林寿. 连通度量空间的映象[J]. 数学年刊A辑(中文版), 2005, 0(3) |
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| 作者姓名： | 林寿 |
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| 作者单位： | 漳州师范学院数学系 福建漳州 |
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| 基金项目： | 国家自然科学基金(No．10271026)，福建省自然科学基金(No.F0310010)资助的项目． |
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| 摘 要： | 拓扑空间X称为s连通,若X不能表示为两个非空的不相交的序列开集之并.本文纠正了A.Fedeli 和A.Le Donne关于连通度量空间映象的错误论证,证明了s连通性可刻画为连通度量空间的连续的序列覆盖映象,从而导出连通的序列空间(或FrEchet空间)可刻画为连通度量空间的商映象(或伪开映象),回答了V.V.Tkachuk在Proc.Amer.Math Soc.上提出的问题.
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| 关 键 词： | s连通性 连通性 道路连通性 序列空间 度量空间 商映射 序列覆盖映射 |
THE IMAGES OF CONNECTED METRIC SPACES |
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| LIN Shou. THE IMAGES OF CONNECTED METRIC SPACES[J]. Chinese Annals of Mathematics, 2005, 0(3) |
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| Authors: | LIN Shou |
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| Affiliation: | LIN Shou Department of Mathematics,Zhangzhou Teachers' College,Zhangzhou 363000,Fujian,China, Department of Mathematics,Fujian Normal University,Fuzhou 350007,China. |
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| Abstract: | A space is called s-connected if it cannot be represented as the union of two non-empty disjoint sequentially closed subsets. This paper corrects some mistakes about images of connected metric spaces by A. Fedeli and A. Le Donne, and shows that a space is an .sconnected space if and only if it is a continuous and sequence-covering image of a connected metric space, and a space is a connected and sequential space if and only if it is a quotient image of a connected metric space, which answers a question posed by V. V. Tkachuk in Proc. Amer. Math. Soc. |
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| Keywords: | s-conneetedness Connectedness Pathwise connectedness Sequential spaces Metric spaces Quotient mappings Sequence-covering mappings |
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