The open-point and bi-point-open topologies on C(X): Submetrizability and cardinal functions

In [9], two new kinds of topologies called the open-point topology and the bi-point-open topology on C(X)C(X), the set of all real-valued continuous functions on a Tychonoff space X  , have been introduced and their separation and countability properties have been studied. In the present paper, we study the submetrizability and cardinal functions such as extent, cellularity, weight, pseudocharacter, character and tightness of the spaces C(X)C(X) equipped with the open-point and bi-point-open topologies.