Pairings of function spaces

Pairings and copairings of topological spaces induce pairings of function spaces. These induced pairings of function spaces are studied. For this purpose, the C -open topology of function spaces is studied for subcategories C of T op . It is shown that the C -open topology enjoys good properties for homotopy theory. Making use of the C -open topology, theory of induced pairings is established and fundamental results on pairings which deduce various commutativity properties of elements in homotopy set are extended to function spaces.