A study concerning splitting and jointly continuous topologies on <i>C</i>(<i>Y</i>, <i>Z</i>)

Abstract

Let Y and Z be two xed topological spaces and C (Y,Z) the set of all continuous maps from Y into Z. We construct and study topologies on C(Y,Z) that we call F_n(T_n)-family-open topologies. Furthermore, we find necessary and sufficient conditions such that these topologies to be splitting and jointly continuous. Finally, we present questions concerning a further study on this area.

Keywords: Function spaces, splitting topology, jointly continuous topology