Equivalence of completeness and contraction property

@inproceedings{Xiang2007EquivalenceOC,
  title={Equivalence of completeness and contraction property},
  author={Shuwen Xiang},
  year={2007}
}
In this paper, we consider the completeness and the contraction property in metric spaces and show that the contraction property implies Lipschitz-completeness or arcwise-completeness in a metric space. However, in a metric space, the contraction property does not imply the usual completeness. We prove that a locally Lipschitz-connected metric space has the contraction property if and only if it is Lipschitz-complete and that a locally arcwise-connected metric space is arcwise-complete if and… CONTINUE READING

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