A study of function space topologies for multifunctions


  • Ankit Gupta University of Delhi
  • Ratna Dev Sarma University of Delhi




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


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. 


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Author Biographies

Ankit Gupta, University of Delhi

Department of Mathematics

Ratna Dev Sarma, University of Delhi

Department of Mathematics, Rajdhani College


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How to Cite

A. Gupta and R. D. Sarma, “A study of function space topologies for multifunctions”, Appl. Gen. Topol., vol. 18, no. 2, pp. 331–344, Oct. 2017.



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