The compact-open topology: A new perspective

This paper studies the compact-open topology on the set KC ( X ) of all real-valued functions defined on a Tychonoff space, which are continuous on compact subsets of X. In addition to metrizability, separability and second countability of this topology on KC ( X ) , various kinds of topological properties of this topology are studied in detail. Actually the motivation for studying the compact-open topology on KC ( X ) lies in the attempt of having a simpler proof for the characterization of a completeness property of the compact-open topology on C ( X ) , the set of all real-valued continuous functions on X.