A study of function space topologies for multifunctions

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)...

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Vydané v:Applied general topology Ročník 18; číslo 2; s. 331 - 344
Hlavní autori: Gupta, Ankit, Sarma, Ratna Dev
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Universitat Politècnica de València 01.01.2017
Predmet:
admissibil- ity
continuous convergence
function space
multifunction
splittingness
topology
ISSN:1576-9402, 1989-4147
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Shrnutí: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. 
ISSN:1576-9402
1989-4147
DOI:10.4995/agt.2017.7149