Ambiguous loci of the farthest distance mapping from compact convex sets
Studia Mathematica, Tome 112 (1995) no. 2, p. 99.

Voir la notice de l'article dans European Digital Mathematics Library

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 K 0 the set of all X ∈ K() such that the farthest distance mapping a ↦ M X ( a ) is multivalued on a dense subset of . It is proved that K 0 is a residual dense subset of K().
Classification : 52A07, 51K05
Mots-clés : convex sets, farthest points, distance mapping 
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     title = {Ambiguous loci of the farthest distance mapping from compact convex sets},
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F. De Blasi; J. Myjak. Ambiguous loci of the farthest distance mapping from compact convex sets. Studia Mathematica, Tome 112 (1995) no. 2, p. 99. https://geodesic-test.mathdoc.fr/item/STUMA_1995__112_2_216147/