The bounded-open topology on function spaces

For any regular space Z It is shown, 1) that the bounded-open topology T on C(Y,Z) is splitting and it is also the smallest jointly continuous topology whenever Y is locally bounded, 2) if Y is locally bounded or if X × Y is a boundedly generated space, then there is a natural bijection on C(X × Y,Z) onto C(X,(C(Y,Z),T_eo) which is actually a homeomorphism with respect to the bounded-open topology on both function spaces, 3) The path components of (C(Y,Z),T_eo) are exactly its homotopy classes whenever Y is boundedly generated, 4) The bounded-open topology Teo induces contravariant and covariant Homotopy preserving function-space functors. Further, 5) T_eo reduces to the compact-open topology t_co whenever the domain Y is regular; but in general, T_eo is finer than T_co (assuming the domain is Hausdorff or the range is either Hausdorff or regular).