Graph topologies on closed multifunctions

Giuseppe Di Maio; Enrico Meccariello; Somashekhar Naimpally

doi:10.4995/agt.2003.2044

Authors

Giuseppe Di Maio Seconda Università degli Studi di Napoli
Enrico Meccariello Università del Sannio
Somashekhar Naimpally

DOI:

https://doi.org/10.4995/agt.2003.2044

Keywords:

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

Abstract

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.

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Author Biographies

Giuseppe Di Maio, Seconda Università degli Studi di Napoli

Dipartimento di Matematica

Enrico Meccariello, Università del Sannio

Facoltà di Ingegneria

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