| Banach压缩映象原理与空间完备性 |
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| 引用本文： | 向叔文.Banach压缩映象原理与空间完备性[J].系统科学与数学,1997,17(4):307-310. |
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| 作者姓名： | 向叔文 |
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| 作者单位： | 浙江大学应用数学系 杭州，310027，贵州工业大学应用数学研究所，550003 |
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| 摘 要： | 本文揭示了Banach压缩映象原理与空间完备性的关系,证明了在具有一致局部连通性的距离空间中,压缩映象原理与空间完备性仍然等价.
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| 关 键 词： | 压缩映象原理 完备性 一致局部连通 距离空间 |
BANACH CONTRACTION PRINCIPLE AND COMPLETENESS |
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| Xiang Shuwen.BANACH CONTRACTION PRINCIPLE AND COMPLETENESS[J].Journal of Systems Science and Mathematical Sciences,1997,17(4):307-310. |
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| Authors: | Xiang Shuwen |
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| Institution: | Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310027) |
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| Abstract: | In this paper, we study a further relation between the Banach contraction principle and the completeness of spaces. We prove that for a metric space with uniformly local connectedness the Banach contraction principle is equivalent to the completeness. |
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| Keywords: | Contraction principle completeness uniformly local connectedness metric space |
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