Literature cited
V. L. 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).
L. P. Vlasov, “Approximative properties of sets in linear normed spaces,” Usp. Mat. Nauk,28, No. 6, 3–66 (1973).
E. V. Oshman, “Characteristics of subspaces with continuous metric projections in a linear normed space,” Dokl. Akad. Nauk SSSR,207, No. 2, 292–295 (1972).
F. Deutsch, W. Pollul, and I. Singer, “On sets-valued metric projections, Hahn-Banach extension maps, and spherical image maps,” Duke Math. J.,40, No. 2, 355–370 (1973).
P. D. Morris, “Metric projections onto subspaces of finite codimension,” Duke Math. J.,35, No. 4, 797–808 (1968).
E. V. Oshman, “On the continuity of the metric projection onto a subspace of finite defect in a space of continuous functions,” Mat. Zametki,19, No. 4, 531–539 (1976).
A. L. Garkavi, “On compacta admitting Chebyshev systems of measures,” Mat. Sb.,74, No. 2, 209–217 (1967).
A. L. Garkavi, “Helley's problem and best approximation in a space of continuous functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,31, No. 3, 641–656 (1967).
N. Dunford and J. T. Schwartz, Linear Operators, Part 1, Wiley (1958).
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Translated from Matematicheskie Zametki, Vol. 27, No. 4, pp. 597–606, April, 1980.
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Oshman, E.V. Continuity of metric projection onto a Chebyshev subspace of finite codimension in a space of continuous functions. Mathematical Notes of the Academy of Sciences of the USSR 27, 293–298 (1980). https://doi.org/10.1007/BF01140531
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DOI: https://doi.org/10.1007/BF01140531