Topological and functional analytic properties of the compact-Gδ-open topology on C(X)

In this paper, we study extensively the compact-Gδ-open topology on the set C(X) of all real-valued continuous functions on a Tychonoff space X. In particular, we study the induced map, submetrizability, completeness properties, countability properties, and nuclear and reflexive properties of the compact-Gδ-open topology on C(X).