Abstract:Following the paper [BDC1], further relations between the classical topologies on function spaces and new ones induced by hyperspace topologies on graphs of functions are introduced and further characterizations of boundedly \text {$UC$} spaces are given.
Keywords: \text {$UC$} space, boundedly \text {$UC$} space, boundedly compact space, compact-open topology, topology of uniform convergence on bounded sets, Attouch-Wets topology, bounded proximal topology
AMS Subject Classification: Primary 54C35