Set-open topologies on function spaces
Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2018-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/7630 |
| _version_ | 1819204590368718848 |
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| author | Wafa Khalaf Alqurashi Liaqat Ali Khan Alexander V. Osipov |
| author_facet | Wafa Khalaf Alqurashi Liaqat Ali Khan Alexander V. Osipov |
| author_sort | Wafa Khalaf Alqurashi |
| collection | DOAJ |
| description | Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological space as well as for Y = R. Further, we consider the parallel notion of quasi-uniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλ-closedness and right Uλ-K-completeness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasi-uniform space. We include some counter-examples to justify our comments. |
| first_indexed | 2024-12-23T04:38:14Z |
| format | Article |
| id | doaj.art-cf9d9416a23b4594b97ebde85f432689 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-23T04:38:14Z |
| publishDate | 2018-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-cf9d9416a23b4594b97ebde85f4326892022-12-21T17:59:51ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472018-04-01191556410.4995/agt.2018.76306753Set-open topologies on function spacesWafa Khalaf Alqurashi0Liaqat Ali Khan1Alexander V. Osipov2Umm Al-Qura UniversityQuaid-i-Azam UniversityUral State University of EconomicsLet X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological space as well as for Y = R. Further, we consider the parallel notion of quasi-uniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλ-closedness and right Uλ-K-completeness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasi-uniform space. We include some counter-examples to justify our comments.https://polipapers.upv.es/index.php/AGT/article/view/7630set-open topologypseudocompact-open topologyC-compact- open topologyquasi-uniform convergence topologyright K- completenessα-continuous function |
| spellingShingle | Wafa Khalaf Alqurashi Liaqat Ali Khan Alexander V. Osipov Set-open topologies on function spaces Applied General Topology set-open topology pseudocompact-open topology C-compact- open topology quasi-uniform convergence topology right K- completeness α-continuous function |
| title | Set-open topologies on function spaces |
| title_full | Set-open topologies on function spaces |
| title_fullStr | Set-open topologies on function spaces |
| title_full_unstemmed | Set-open topologies on function spaces |
| title_short | Set-open topologies on function spaces |
| title_sort | set open topologies on function spaces |
| topic | set-open topology pseudocompact-open topology C-compact- open topology quasi-uniform convergence topology right K- completeness α-continuous function |
| url | https://polipapers.upv.es/index.php/AGT/article/view/7630 |
| work_keys_str_mv | AT wafakhalafalqurashi setopentopologiesonfunctionspaces AT liaqatalikhan setopentopologiesonfunctionspaces AT alexandervosipov setopentopologiesonfunctionspaces |