Non-symmetric convergence and regularity
We study regularity in quasi-convergence spaces and biconvergence spaces. We show that a notion weaker than the usually considered pairwise regularity is sufficient in important applications. This regularity can be defined in terms of closures of pair filters or by a diagonal condition. We show its...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2025-04-01
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| Series: | Applied General Topology |
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| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/22432 |
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| _version_ | 1849766425213796352 |
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| author | Gunther Jäger |
| author_facet | Gunther Jäger |
| author_sort | Gunther Jäger |
| collection | DOAJ |
| description | We study regularity in quasi-convergence spaces and biconvergence spaces. We show that a notion weaker than the usually considered pairwise regularity is sufficient in important applications. This regularity can be defined in terms of closures of pair filters or by a diagonal condition. We show its appropriateness by characterizing it in terms of continuous convergence and in terms of extensions of continuous mappings. |
| format | Article |
| id | doaj-art-dea09bf0bf2a40fca005a1121323a24e |
| institution | DOAJ |
| issn | 1576-9402 1989-4147 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj-art-dea09bf0bf2a40fca005a1121323a24e2025-08-20T03:04:35ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472025-04-0126144746710.4995/agt.2025.2243221622Non-symmetric convergence and regularityGunther Jäger0https://orcid.org/0000-0002-1495-4564University of Applied Sciences StralsundWe study regularity in quasi-convergence spaces and biconvergence spaces. We show that a notion weaker than the usually considered pairwise regularity is sufficient in important applications. This regularity can be defined in terms of closures of pair filters or by a diagonal condition. We show its appropriateness by characterizing it in terms of continuous convergence and in terms of extensions of continuous mappings.https://polipapers.upv.es/index.php/AGT/article/view/22432quasi-convergence spaceregularityextension of mappingscontinuous convergencebiconvergence convergence space |
| spellingShingle | Gunther Jäger Non-symmetric convergence and regularity Applied General Topology quasi-convergence space regularity extension of mappings continuous convergence biconvergence convergence space |
| title | Non-symmetric convergence and regularity |
| title_full | Non-symmetric convergence and regularity |
| title_fullStr | Non-symmetric convergence and regularity |
| title_full_unstemmed | Non-symmetric convergence and regularity |
| title_short | Non-symmetric convergence and regularity |
| title_sort | non symmetric convergence and regularity |
| topic | quasi-convergence space regularity extension of mappings continuous convergence biconvergence convergence space |
| url | https://polipapers.upv.es/index.php/AGT/article/view/22432 |
| work_keys_str_mv | AT guntherjager nonsymmetricconvergenceandregularity |