Smoothness of a typical convex function

Vlastimil Klíma; Ivan Netuka

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Robert J. MacG. Dawson (1987)

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Properties of typical bounded closed convex sets in Hilbert space.

de Blasi, F.S., Zhivkov, N.V. (2005)

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Ambiguous loci of the farthest distance mapping from compact convex sets

F. De Blasi, J. Myjak (1995)

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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 $a \mapsto M_{X} (a)$ is multivalued on a dense subset of . It is proved that $K^{0}$ is a residual dense subset of K().

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