A study of function space topologies for multifunctions

[EN] Function space topologies are investigated for the class ofcontinuousmultifunctions. Using the notion of continuous convergence, splitting-ness and admissibility are discussed for the topologies on continuousmultifunctions. The theory of net of sets is further developed for thispurpose. The(τ,μ)-topology on the class of continuous multifunctionsis found to be upper admissible, while the compact-open topology isupper splitting. The point-open topology is the coarsest topology whichis coordinately admissible, it is also the finest topology which is coor-dinately splitting.