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ArticleOriginal scientific text

Title

Ambiguous loci of the farthest distance mapping from compact convex sets

Authors 1, 2

Affiliations

  1. Centro Matematico V. Volterra, Università di Roma II, Via della Ricerca Scientifica, 00133 Roma, Italy
  2. Dipartimento di Matematica, Università dell'Aquila, Via Vetoio, 67010 Coppito (L'Aquila), Italy

Abstract

Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by K0 the set of all X ∈ K() such that the farthest distance mapping a↦MX(a) is multivalued on a dense subset of . It is proved that K0 is a residual dense subset of K().

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Studia Mathematica
1994-1995/112/2
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Pages:
99-107
Main language of publication
English
Received
1991-10-18
Accepted
1992-12-14
Published
1995
Exact and natural sciences