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 |
| Summary: | 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. |
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| ISSN: | 1576-9402 1989-4147 |