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.
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