Literature cited
N. V. Efimov and S. B. Stechkin, “Approximate compactness and Chebyshev sets,” Dokl. Akad. Nauk SSSR,140, No. 3, 522–524 (1961).
L. P. Vlasov, “Approximate properties of sets in normed linear spaces,” Usp. Mat. Nauk,28, No. 6, 3–66 (1973).
R. C. James, “Characterizations of reflexivity,” Stud. Math.,23, No. 3, 205–216 (1964).
Ka-Sing Lau, “Almost Chebyshev subsets in reflexive Banach spaces,” Indiana Univ. Math. J.,27, No. 5, 791–795 (1978).
S. V. Konyagin, “On approximate properties of closed sets in Banach spaces and characterizations of strictly convex spaces,” Dokl. Akad. Nauk SSSR,251, No. 2, 276–280 (1980).
M. Edelstein and A. C. Thompson, “Some results on nearest points and support properties of convex sets in c0,” Pac. J. Math.,40, No. 3, 553–560 (1972).
S. Cobzas, “Antiproximinal sets in Banach spaces of c-type,” Math. Rev. Anal. Numer. Theor. Approx.,7, No. 2, 141–142 (1978).
K. Yoshida, Functional Analysis, Springer-Verlag, New York-Berlin (1968).
C. Kuratowski, Topology, Vol. 1, Academic Press (1966).
S. B. Stechkin, “Approximate properties of sets in normed linear spaces,” Rev. Math. Pure Appl.,8, No. 1, 5–18 (1963).
E. V. Oshman, “A characterization of subspaces with continuous metric projection in a normed linear space,” Dokl. Akad. Nauk SSSR,207, No. 2, 292–295 (1972).
P. Kenderov, “Points of single-valuedness of multivalued metric projections,” Dokl. Bol. Akad. Nauk,29, No. 6, 773–775 (1976).
E. V. Oshman, “On the continuity of the metric projection in the space C(Q),” Dokl. Akad. Nauk SSSR,251, No. 5, 1063–1066 (1980).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 33, No. 5, pp. 641–655, May, 1983.
Rights and permissions
About this article
Cite this article
Konyagin, S.V. Sets of points of nonemptiness and continuity of the metric projection. Mathematical Notes of the Academy of Sciences of the USSR 33, 331–338 (1983). https://doi.org/10.1007/BF01158278
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01158278