@article{Alqurashi_Khan_Osipov_2018, title={Set-open topologies on function spaces}, volume={19}, url={https://ojs.upv.es/index.php/AGT/article/view/7630}, DOI={10.4995/agt.2018.7630}, abstractNote={<p>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 âŠ† 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 âŠ† 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.</p>}, number={1}, journal={Applied General Topology}, author={Alqurashi, Wafa Khalaf and Khan, Liaqat Ali and Osipov, Alexander V.}, year={2018}, month={Apr.}, pages={55–64} }