A Solution to the Completion Problem for Quasi-Pseudometric Spaces
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 sen...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/278381 |
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| _version_ | 1849402621145645056 |
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| author | Athanasios Andrikopoulos |
| author_facet | Athanasios Andrikopoulos |
| author_sort | Athanasios Andrikopoulos |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9676adc1460c4ea8a9a762fb1c123d29 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9676adc1460c4ea8a9a762fb1c123d292025-08-20T03:37:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/278381278381A Solution to the Completion Problem for Quasi-Pseudometric SpacesAthanasios Andrikopoulos0Department of Economics, University of Ioannina, P.O. Box 1186, 45110 Ioannina, GreeceThe 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.http://dx.doi.org/10.1155/2013/278381 |
| spellingShingle | Athanasios Andrikopoulos A Solution to the Completion Problem for Quasi-Pseudometric Spaces International Journal of Mathematics and Mathematical Sciences |
| title | A Solution to the Completion Problem for Quasi-Pseudometric Spaces |
| title_full | A Solution to the Completion Problem for Quasi-Pseudometric Spaces |
| title_fullStr | A Solution to the Completion Problem for Quasi-Pseudometric Spaces |
| title_full_unstemmed | A Solution to the Completion Problem for Quasi-Pseudometric Spaces |
| title_short | A Solution to the Completion Problem for Quasi-Pseudometric Spaces |
| title_sort | solution to the completion problem for quasi pseudometric spaces |
| url | http://dx.doi.org/10.1155/2013/278381 |
| work_keys_str_mv | AT athanasiosandrikopoulos asolutiontothecompletionproblemforquasipseudometricspaces AT athanasiosandrikopoulos solutiontothecompletionproblemforquasipseudometricspaces |