Abstract and Applied Analysis
Volume 2005 (2005), Issue 4, Pages 423-436
doi:10.1155/AAA.2005.423
Properties of typical bounded closed convex sets in Hilbert space
F.S. de Blasi1
and N.V. Zhivkov2
1Dipartimento di Matematica, Università di Roma II, Via della Ricerca Scientifica, Roma 00133, Italy
2Institute of Mathematics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
Abstract
For a nonempty separable convex subset X of a Hilbert space ℍ(Ω), it is typical (in the sense of Baire category) that a bounded closed convex set C⊂ℍ(Ω) defines an m-valued metric antiprojection (farthest point mapping) at the points of a dense subset of X, whenever m is a positive integer such that m≤dimX+1.