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Strict sums and semicontinuity below metric projections in linear normed spaces. (English) Zbl 0408.41019

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems
Full Text: DOI
[1] L. P. Vlasov, ”Approximative properties of sets in linear normed spaces,” Usp. Mat. Nauk,28, No. 6, 3–66 (1973). · Zbl 0293.41031
[2] L. P. Vlasov, ”Chebyshev sets and some of their generalizations,” Mat. Zametki,3, No. 1, 59–69 (1968). · Zbl 0155.45401
[3] B. Brosqwski and F. Deutsh, ”Radial continuity of set-valued metric projections,” J. Approx. Theory,11, No. 3, 236–253 (1974). · Zbl 0283.41014 · doi:10.1016/0021-9045(74)90016-1
[4] D. E. Wulbert, Continuity of Metric Projections, Approximation Theory in a Normed Linear Lattice, Thesis, Univ. Texas Comp. Center, Austin (1966).
[5] V. A. Koshcheev, ”Connectivity and some approximative properties of sets in linear normed spaces,” Mat. Zametki,17, No. 2, 193–204 (1975).
[6] E. V. Oshman, ”Chebyshev sets and continuity of metric projections,” Izv. Vyssh. Uchebn. Zaved., Mat.,9, 78–82 (1970).
[7] M. M. Day, Normed Linear Spaces, Academic Press, New York (1962). · Zbl 0100.10802
[8] E. V. Oshman and N. V. Nevesenko, ”Continuity of multivalued metric projections in linear normed spaces,” Dokl. Akad. Nauk SSSR,223, No. 5, 1064–1066 (1975).
[9] I. Singer, ”Some remarks on approximative compactness,” Rev. Rounu Math. Pures Apll.,9, No. 2, 167–177 (1964). · Zbl 0166.39405
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