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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Bibliographic Details
Published in:	Applied general topology Vol. 19; no. 1; pp. 55 - 64
Main Authors:	Alqurashi, Wafa Khalaf, Khan, Liaqat Ali, Osipov, Alexander V.
Format:	Journal Article
Language:	English
Published:	Universitat Politècnica de València 01.01.2018
Subjects:	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
Online Access:	Get full text
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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.
ISSN:	1576-9402 1989-4147
DOI:	10.4995/agt.2018.7630