TY - JOUR
AU - Alqurashi, Wafa Khalaf
AU - Khan, Liaqat Ali
AU - Osipov, Alexander V.
PY - 2018/04/02
Y2 - 2022/12/08
TI - Set-open topologies on function spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 19
IS - 1
SE -
DO - 10.4995/agt.2018.7630
UR - http://ojs.upv.es/index.php/AGT/article/view/7630
SP - 55-64
AB - <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>
ER -