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On the topology of D -metric spaces and generation of D -metric spaces from metric spaces

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  • S. V. R. Naidu
  • K. P. R. Rao
  • N. Srinivasa Rao

Abstract

An example of a D -metric space is given, in which D -metric convergence does not define a topology and in which a convergent sequence can have infinitely many limits. Certain methods for constructing D -metric spaces from a given metric space are developed and are used in constructing (1) an example of a D -metric space in which D -metric convergence defines a topology which is T 1 but not Hausdorff, and (2) an example of a D -metric space in which D -metric convergence defines a metrizable topology but the D -metric is not continuous even in a single variable.

Suggested Citation

  • S. V. R. Naidu & K. P. R. Rao & N. Srinivasa Rao, 2004. "On the topology of D -metric spaces and generation of D -metric spaces from metric spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-22, January.
    • Handle: RePEc:hin:jijmms:132976
    DOI: 10.1155/S0161171204311257
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