Separability of path spaces under the open-point and bi-point-open topologies

In [3], two new kinds of topologies called the open-point topology and bi-point-open on C(X), set all real-valued continuous functions a Tychonoff space X, have been introduced. this article, we study separability P(X), maps [0; 1] into Hausdorff with topologies. Our result also demonstrates, claim made in that both domain as well codomain play significant roles construction