We study the approximation of multivalued functions in the Fell topology by means of single valued continuous functions or minimal upper semicontinuous compact-valued maps. We give a partial answer to Question 5.5 in [R.A. McCoy, Comparison of hyperspace and function space topologies. in: G. Di Maio, L. Hola, (Eds.). Recent Progress in Function Spaces. in: Quad. Mat., vol. 3, Aracne Editrice, Caserta. 1998, pp. 241-251] and to Question 7 in [R.A. McCoy, Fell topology and uniform topology on compacta on spaces of multifunctions, Rostock. Math. Kolloq. 51 (1997) 127-136]. (C) 2008 Elsevier B.V. All rights reserved.
Approximation by continuous functions in the Fell topology
ARTICO, GIULIANO;MARCONI, UMBERTO;MORESCO, ROBERTO
2008
Abstract
We study the approximation of multivalued functions in the Fell topology by means of single valued continuous functions or minimal upper semicontinuous compact-valued maps. We give a partial answer to Question 5.5 in [R.A. McCoy, Comparison of hyperspace and function space topologies. in: G. Di Maio, L. Hola, (Eds.). Recent Progress in Function Spaces. in: Quad. Mat., vol. 3, Aracne Editrice, Caserta. 1998, pp. 241-251] and to Question 7 in [R.A. McCoy, Fell topology and uniform topology on compacta on spaces of multifunctions, Rostock. Math. Kolloq. 51 (1997) 127-136]. (C) 2008 Elsevier B.V. All rights reserved.
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