Abstract and Applied Analysis
Volume 2005 (2005), Issue 4, Pages 423-436
Properties of typical bounded closed convex sets in Hilbert space
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.
For a nonempty separable convex subset of a Hilbert space , it is typical (in the sense of Baire category)
that a bounded closed convex set defines an -valued metric antiprojection (farthest point
mapping) at the points of a dense subset of , whenever is a positive integer such that .