A Solution to the Completion Problem for Quasi-Pseudometric Spaces

Athanasios Andrikopoulos

International Journal of Mathematics and Mathematical Sciences, 2013, vol. 2013, 1-12

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:278381

DOI: 10.1155/2013/278381

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