Set-open topologies on function spaces

• Autores: Wafa Khalaf Alqurash, Liaqat Ali Khan, Alexander V. Osipov
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 19, Nº. 1, 2018, págs. 55-64
• Idioma: inglés
• DOI: 10.4995/agt.2018.7630
• Enlaces
  • Texto completo
• Resumen

  • 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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