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

S. V. R. Naidu, K. P. R. Rao and N. Srinivasa Rao

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-22

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:132976

DOI: 10.1155/S0161171204311257

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