A Solution to the Completion Problem for Quasi-Pseudometric Spaces | Zendy

Athanasios Andrikopoulos | Zendy

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A Solution to the Completion Problem for Quasi-Pseudometric Spaces

Author(s) -

Athanasios Andrikopoulos

Publication year - 2013

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2013/278381

Subject(s) - mathematics , completeness (order theory) , equivalence (formal languages) , matrix (chemical analysis) , sequence (biology) , path (computing) , combinatorics , discrete mathematics , algebra over a field , pure mathematics , mathematical analysis , materials science , biology , computer science , composite material , genetics , programming language

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 T0 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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