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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 51, Pages 2719-2740
http://dx.doi.org/10.1155/S0161171204311257

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

1Department of Applied Mathematics, Andhra University, Visakhapatnam 530 003, India
2Department of Applied Mathematics, Nagarjuna University Post Graduate (N.U.P.G.) Centre, Acharya Nagarjuna University, Nuzvid 521 201, India

Received 20 November 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 T1 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.