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BANACH CONTRACTION PRINCIPLE AND COMPLETENESS
Banach压缩映象原理与空间完备性

Keywords: Contraction principle,completeness,uniformly local connectedness,metric space
压缩映象原理
,完备性,一致局部连通,距离空间

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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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