A study of function space topologies for multifunctions

Ankit Gupta, Ratna Dev Sarma

Abstract

Function space topologies are investigated for the class of continuous multifunctions. Using the notion of continuous convergence, splittingness and admissibility are discussed for the topologies on continuous multifunctions. The theory of net of sets is further developed for this purpose. The (τ,μ)-topology on the class of continuous multifunctions is found to be upper admissible, while the compact-open topology is upper splitting. The point-open topology is the coarsest topology which is coordinately admissible, it is also the finest topology which is coordinately splitting. 


Keywords

multifunction; topology; function space; continuous convergence; splittingness; admissibility

Subject classification

54C35; 54A05; 54C60

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References

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