The \(Clp\)-compact-open topology on function spaces

Abstract

In this paper, we introduce (weak) \(clp\)-compact-open topology on \(C(X)\) and compare this topology withcompact-open topology and  the topology of uniform convergence. Then we examine metrizability, completeness and countability properties of the weak \(clp\)-compact-open topology on \(C^∗(X)\).