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Uniform structures on hyperspaces and uniform topologies on spaces of multifunctions

Del Prete I., Di Iorio M., Holá Ľ.

Demonstratio Mathematica

2003

Vol. 36, nr 4

985--1000

The aim of this paper is to study uniform and topological structures on spaces of multifunctions. Uniform structures on hyperspaces compatible with the Fell, the Wijsman and the Hausdorff metric topology respectively are studied and the links between them are explored. Topologies induced by the above uniformities on spaces of multifunctions are considered and compared. Also connections between uniform convergence of multifunctions and their equi-semicontinuity are investigated.