Abstract
The connectedness of certain classes of suns is studied. In particular, it is proved that a compact sun is connected in a normed space. Every γ sun is connected in a uniformly non-square Banach space.
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D. E. Wulbert, “Continuity of metric projections, approximation theory in a normed linear lattice,” The University of Texas Computation Center, Austin (1969).
D. E. Wulbert, “Continuity of metric projections,” Trans. Amer. Math. Soc.,134, No. 2, 335–341 (1968).
D. E. Wulbert, Structure of Tchebyshev Sets, General Topology and Its Relations to Modern Analysis and Algebra II, Proc. Second Prague Top. Symp., 356–358 (1966).
L. P. Vlasov, “Approximation properties of sets in normed linear spaces,∝ Usp. Matem. Nauk,28, No. 6, 3–66 (1973).
L. P. Vlasov, “Tchebychev sets and certain generalizations of them,” Matem. Zametki,3, No. 1, 59–69 (1968).
V. A. Koshcheev, “Connectedness and certain approximative properties in normed linear spaces,” Matem. Zametki,17, No. 2, 193–204 (1975).
N. V. Efimov and S. B. Stechkin, “Some properties of Tchebychev sets,” Dokl. Akad. Nauk SSSR,118, No. 1, 17–19 (1958).
B. Brosowski and R. Wegmann, “Charakterisierung bester Approximationen in normierten Vektorraümen,” J. Approx. Th.,3, No. 4, 369–397 (1970).
R. C. James, “Uniformly nonsquare Banach spaces,” Ann. of Math.,80, No. 3, 542–550 (1964).
L. P. Vlasov, “Almost convex and Tchebychev sets,” Matem. Zametki,8, No. 5, 545–550 (1970).
E. V. Oshman, “Tchebychev sets and the continuity of the metric projection,” Izv. Vyssh. Uchebn. Zaved., Matematika,9, 78–82 (1970).
M. M. Day, Normed Linear Spaces, Springer-Verlag (1973).
L. P. Vlasov,“Approximative properties of sets in Banach spaces,” Matem. Zametki,7, No. 5, 593–604 (1970).
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Translated from Matematicheskii Zametki, Vol. 19, No. 2, pp. 267–278, February, 1976.
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Koshcheev, B.A. Connectedness and solar properties of sets in normed linear spaces. Mathematical Notes of the Academy of Sciences of the USSR 19, 158–164 (1976). https://doi.org/10.1007/BF01098750
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DOI: https://doi.org/10.1007/BF01098750