Ambiguous loci of the farthest distance mapping from compact convex sets

• Autorzy: F. S. De Blasi , J. Myjak
• Języki publikacji: EN

Abstrakty

EN

Let 𝔼 be a strictly convex separable Banach space of dimension at least 2. Let K(𝔼) be the space of all nonempty compact convex subsets of 𝔼 endowed with the Hausdorff distance. Denote by $K^0$ the set of all X ∈ K(𝔼) such that the farthest distance mapping $a ↦ M_X(a)$ is multivalued on a dense subset of 𝔼. It is proved that $K^0$ is a residual dense subset of K(𝔼).

Kategorie tematyczne

• 52A07: Convex sets in topological vector spaces
• 41A50: Best approximation, Chebyshev systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994-1995
• Tom: 112
• Numer: 2
• Strony: 99-107

Daty

wydano

1995

otrzymano

1991-10-18

poprawiono

1992-12-14

Twórcy

autor

F. S. De Blasi

• Centro Matematico V. Volterra, Università di Roma II, Via della Ricerca Scientifica, 00133 Roma, Italy

autor

J. Myjak

• Dipartimento di Matematica, Università dell'Aquila, Via Vetoio, 67010 Coppito (L'Aquila), Italy

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