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

Received 22 November 2003

Copyright © 2005 F. S. de Blasi and N. V. Zhivkov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.