Literature cited
L. P. Vlasov, “On Chebyshev and approximatively compact sets,” Mat. Zametki,1, No. 2, 191–198 (1967).
E. Asplund, “Chebyshev sets in Hilbert space,” Trans. Am. Math. Soc.,144, 235–240 (1969).
L. P. Vlasov, “Approximative properties of sets in normed linear spaces,” Usp. Mat. Nauk,28, No. 6, 3–66 (1973).
S. V. Konyagin, “Approximative properties of closed sets in Banach spaces and a characterization of strictly convex spaces,” Dokl. Akad. Nauk SSSR,251, No. 1, 276–279 (1980).
V. Klee, “Convexity of Chebyshev sets,” Math. Ann.,142, No. 3, 292–304 (1961).
N. V. Efimov and S. B. Stechkin, “Some properties of Chebyshev sets,” Dokl. Akad. Nauk SSSR,118, No. 1, 17–19 (1958).
A. L. Garkavi, “On the best net and best section of a set in a normed space,” Izv. Akad. Nauk SSSR, Ser. Mat.,26, No. 1, 87–106 (1962).
M. M. Day, Normed Linear Spaces, Third Ed., Springer-Verlag (1973).
B. B. Panda and O. P. Kapoor, “On equidistant sets in normed linear spaces,” Bull. Aust. Math. Soc.,11, No. 3, 443–454 (1974).
C. A. Kottman and Bor-Luh Lin, “The weak continuity of metric projection,” Michigan Math. J.,17, No. 4, 401–404 (1970).
M. Edelstein, “Farthest points of sets in uniformly convex Banach spaces,” Isr. J. Math.,4, 171–176 (1966).
J. Lindenstrauss, “Weakly compact sets, their topological properties, and the Banach spaces they generate,” Ann. Math. Stud.,69, 235–273 (1972).
V. Zizler, “On extremal structure of weakly locally compact convex sets in Banach spaces,” Comment. Math. Univ. Carolin.,13, No. 1, 53–61 (1972).
S. B. Stechkin, “Approximative properties of sets in normed linear spaces,” Rev. Math. Pur. Appl.,8, No. 1, 5–18 (1963).
K. Kuratowski, Topology, Vol. 2, Academic Press (1972).
V. A. Koshcheev, “Connectedness and some approximative properties of sets in normed linear spaces,” Mat. Zametki,17, No. 2, 193–204 (1975).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 31, No. 5, pp. 785–800, May, 1982.
Rights and permissions
About this article
Cite this article
Balaganskii, V.S. Approximative properties of sets in Hilbert space. Mathematical Notes of the Academy of Sciences of the USSR 31, 397–404 (1982). https://doi.org/10.1007/BF01145720
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01145720