Dual topology for the function space topologies for multifunctions are introduced and investigated. It is found that a topology T on C M (Y, Z) is splitting (resp. admissible) if and only if its dual pair (T + , T −) is splitting (resp. admissible). Similarly, the pair (T + , T −) is splitting (resp. admissible) if and only if its dual T(T + , T −) is splitting (resp. admissible).