The C-compact-open topology on function spaces

This paper studies the C-compact-open topology on the set C ( X ) of all real-valued continuous functions on a Tychonoff space X and compares this topology with several well-known and lesser-known topologies. We investigate the properties of the C-compact-open topology on the set C ( X ) such as submetrizability, metrizability, separability and second-countability.