Chinese Quarterly Journal of Mathematics ›› 2013, Vol. 28 ›› Issue (4): 565-572.

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The Completeness of Cone Metric Spaces

  

  1. Department of Mathematics and Information Science, Zhangzhou Normal University
  • Received:2012-03-14 Online:2013-12-30 Published:2023-02-17
  • About author:LI Ke-dian(1956-), male, native of Zhecheng, Henan, a professor of Zhangzhou Normal Univer- sity, engages in general topology.
  • Supported by:
    Supported by the National Natural Science Foundation of China(10971185,10971186); Supported by the Research Fund for Higher Education of Fujian Province(JK2011031)

Abstract: Some topological properties of cone metric spaces are discussed and proved that every cone metric space (X; d) is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ∈ E; 0 《 c contains a set of diameter less that c has non-empty intersection.


Key words: compactness, completeness, cauchy sequence, cone metric space 

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