Article

A study concerning splitting and jointly continuous topologies on C(Y,Z)

Published in: Quaestiones Mathematicae
Volume 39 , issue 3 , 2016 , pages: 363–379

DOI: 10.2989/16073606.2015.1072855

Author(s): Dimitris Georgiou , , , , Greece , Athanasios Megaritis , , , , Greece , Kyriakos Papadopoulos , , , , Kuwait , Vasilios Petropoulos , , , , Greece

Keywords: 54C35 , Function spaces , splitting topology , jointly continuous topology

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Abstract

Let Y and Z be two fixed 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 w^{e call F} n(τn)-family-open topologies. Furthermore, we find necessary and suﬃcientconditions such that these topologies to be splitting and jointly continuous. Finally, we present questions concerning a further study on this area.

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