Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion
Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completi...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2023-04-01
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| Series: | Applied General Topology |
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| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/18783 |
| _version_ | 1797851625321136128 |
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| author | Gunther Jäger |
| author_facet | Gunther Jäger |
| author_sort | Gunther Jäger |
| collection | DOAJ |
| description | Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces. |
| first_indexed | 2024-04-09T19:20:48Z |
| format | Article |
| id | doaj.art-175cdc8351a64bf59458d796a341f705 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-09T19:20:48Z |
| publishDate | 2023-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-175cdc8351a64bf59458d796a341f7052023-04-05T11:41:08ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472023-04-0124120522710.4995/agt.2023.1878317973Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completionGunther Jäger0https://orcid.org/0000-0002-1495-4564University of Applied Sciences Stralsund, GermanyBased on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces.https://polipapers.upv.es/index.php/AGT/article/view/18783fuzzy topologypair τ-filtercuachy pair τ-filterτ-quasi-cauchy spaceτ-quasi-uniform spacel-metric space |
| spellingShingle | Gunther Jäger Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion Applied General Topology fuzzy topology pair τ-filter cuachy pair τ-filter τ-quasi-cauchy space τ-quasi-uniform space l-metric space |
| title | Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion |
| title_full | Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion |
| title_fullStr | Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion |
| title_full_unstemmed | Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion |
| title_short | Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion |
| title_sort | τ quasi cauchy spaces a non symmetric theory of completeness and completion |
| topic | fuzzy topology pair τ-filter cuachy pair τ-filter τ-quasi-cauchy space τ-quasi-uniform space l-metric space |
| url | https://polipapers.upv.es/index.php/AGT/article/view/18783 |
| work_keys_str_mv | AT guntherjager tquasicauchyspacesanonsymmetrictheoryofcompletenessandcompletion |