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Uniform structures on hyperspaces and uniform topologies on spaces of multifunctions

100%

Del Prete I. , Di Iorio M. , Holá Ľ.

2003

tom 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.

Uniform properties and hyperspaces of metrizable spaces

60%

Costantini C. , Vitolo P.

Journal of Applied Analysis

1999

tom Vol. 5, nr 2

187-196

Two equivalent metrics can be compared, with respect to their uniform properties, in several different ways. We present some of them, and then use one of these conditions to characterize which metrics on a space induce the same lower Hausdorff topology on the hyperspace. Finally, we focus our attention to complete metrics.