A study of function space topologies for multifunctions

Ankit Gupta, Ratna Dev Sarma


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. 


multifunction; topology; function space; continuous convergence; splittingness; admissibil- ity

Subject classification

54C35; 54A05; 54C60.

Full Text:



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1. A study of uniformities on the space of uniformly continuous mappings
Ankit Gupta, Abdulkareem Saleh Hamarsheh, Ratna Dev Sarma, Reny George
Open Mathematics  vol: 18  issue: 1  first page: 1478  year: 2020  
doi: 10.1515/math-2020-0110

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