Cardinality of the metric projection on typical compact sets in Hilbert spaces

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 126, Issue 1, 1999, Pages 37-44

  De Blasi, F S ^a   Zamfirescu, T I ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22444452140     PISSN: 03050041     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0305004198003193     Document Type: Article

References (10)

1. L. E. J. BROUWER. Beweis der Invarianz der Dimensionenzahl. Math. Ann. 70 (1911), 161-105.
2. F. S. DE BLASI. Typical compact convex sets in Hilbert spaces. Serdica Math. J., to appear.
3. A. L. DONTCHEV and T. ZOLEZZI. Well posed optimization problems. Lecture Notes in Mathematics 1543 (Springer-Verlag, 1993).
4. C. MIRANDA. Un'osservazione su un teorema di Brouwer. Boll. Un. Mat. Ital. II (3) (1941), 5-7.
5. I. SINGER. Best approximation in normed linear spaces by elements of linear subspaces (Springer-Verlag, 1970).
6. I. SINGER. The theory of best approximation and functional analysis. (Society for Industrial and Applied Mathematics, Philadelphia, 1974).
7. S. B. STEČKIN. Approximation properties of sets in normed linear spaces. Revue Roumaine, Math. Pures Appl. 8 (1963), 5-18 (Russian).
8. T. I. ZAMFIRESCU. The nearest point mapping is single valued nearly everywhere. Arch. Math. 54 (1990), 563-566.
9. N. V. ZHIVKOV. Compacta with dense ambiguous loci of metric projections and anti-projections. Proc. Amer. Math. Soc. 123 (1995), 3403-3411.
10. N. V. ZHIVKOV. Densely two-valued metric projections in uniformly convex Banach spaces. Set-Valued Analysis 3 (1995), 195-209.