Metrizability and Submetrizability for point-open, open-point and Bi-point-open topologies on C(X,Y) Commun. Korean Math. Soc. Published online May 13, 2022 Barkha . and A. R. PRASANNAN University of Delhi; Department of Mathematics, Maharaja Agrasen College, University of Delhi Abstract : We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X,Y ), where C(X,Y ) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space. Keywords : Point-open topology, Open-point topology, Bi-point-open topology, Metrizability, Submetrizability, Topological group, First countable MSC numbers : 54C35, 54D10, 54H11, 54E35 Full-Text :