If X X and Y Y are topological spaces, the set of all continuous functions from X X into C Y CY , the space of nonempty, compact subsets of Y Y with the finite topology, contains a copy (with singleton sets substituted for points) of Y X {Y^X} , the continuous point-valued functions from X X into Y Y . It is shown that Y X {Y^X} is homeomorphic to this copy contained in ( C Y ) X {(CY)^X} (where all function spaces are assumed to have the compact-open topology) and that, if X X or Y Y is T 2 , ( C Y ) X {T_2},{(CY)^X} is homoemorphic to a subspace of ( C Y ) C X {(CY)^{CX}} . Further, if Y Y is T 2 {T_2} , then these images of Y X {Y^X} and ( C Y ) X {(CY)^X} are closed in ( C Y ) X {(CY)^X} and ( C Y ) C X {(CY)^{CX}} respectively. Finally, it is shown that, under certain conditions, some elements of X Y {X^Y} may be considered as elements of ( C Y ) X {(CY)^X} and that the induced 1 1 - 1 1 function between the subspaces is open.