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

MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems
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[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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