Graph topologies on closed multifunctions

Giuseppe Di Maio, Enrico Meccariello, Somashekhar Naimpally


In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.


Hyperspaces; Function spaces; Graph topologies; Vietoris topology; Fell topology; Uniform convergence on compacta; U-topology; ∆-topology; Proximal ∆-topology; ∆U-topology; Proximal ∆U-topology; Hausdorff-Bourbaki uniformity; ∆-Attouch-Wets filter

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