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International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 278381, 12 pages
http://dx.doi.org/10.1155/2013/278381
Research Article

A Solution to the Completion Problem for Quasi-Pseudometric Spaces

Department of Economics, University of Ioannina, P.O. Box 1186, 45110 Ioannina, Greece

Received 6 September 2013; Accepted 17 November 2013

Academic Editor: R. Lowen

Copyright © 2013 Athanasios Andrikopoulos. 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

The different notions of Cauchy sequence and completeness proposed in the literature for quasi-pseudometric spaces do not provide a satisfactory theory of completeness and completion for all quasi-pseudometric spaces. In this paper, we introduce a notion of completeness which is classical in the sense that it is made up of equivalence classes of Cauchy sequences and constructs a completion for any given quasi-pseudometric space. This new completion theory extends the existing completion theory for metric spaces and satisfies the requirements posed by Doitchinov for a nice theory of completeness.