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Paolo Piccione, Rosella Sampalmieri )JJK?D9AJI ?LAHCA?A =@ KH=JMIE ?LAHCA?A  ?F=?J IAJI

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Paolo Piccione, Rosella Sampalmieri

Attouch-Wets convergence and Kuratowski convergence on compact sets

Comment.Math.Univ.Carolinae 36,3 (1995) 551-562.

Abstract: LetX be a locally connected, b-compact metric space andE a closed subset of X. Let G be the space of all continuous real-valued functions defined on some closed subsets ofE. We prove the equivalence of the τaw and τKc topolo- gies on G, where τaw is the so called Attouch-Wets topology, defined in terms of uniform convergence of distance functionals, andτKc is the topology of Kuratowski convergence on compacta.

Keywords: function spaces, Kuratowski convergence, hyperspaces AMS Subject Classification: 54C35, 54C99

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