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...

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Vydáno v:Applied general topology Ročník 19; číslo 1; s. 55 - 64
Hlavní autoři: Alqurashi, Wafa Khalaf, Khan, Liaqat Ali, Osipov, Alexander V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Universitat Politècnica de València 01.01.2018
Témata:
C-compact- open topology
pseudocompact-open topology
quasi-uniform convergence topology
right K- completeness
set-open topology
α-continuous function
ISSN:1576-9402, 1989-4147
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Abstract 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.
AbstractList 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.
Author Alqurashi, Wafa Khalaf
Khan, Liaqat Ali
Osipov, Alexander V.
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SubjectTerms C-compact- open topology
pseudocompact-open topology
quasi-uniform convergence topology
right K- completeness
set-open topology
α-continuous function
Title Set-open topologies on function spaces
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