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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.

Frechet type theorem and its applications to multifunctions

Kubiś B., Kubiś W.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 2

165-170

We state a Frechet type theorem for measurable maps with values in an almost arcwise connected metrizable space. As an application, we obtain some results on continuous approximation of measurable multifunctions.