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$$\rho$$-continuity of a metric projection onto convex closed sets. (English) Zbl 0425.46008

##### MSC:
 46A55 Convex sets in topological linear spaces; Choquet theory 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 46B10 Duality and reflexivity in normed linear and Banach spaces 46B20 Geometry and structure of normed linear spaces
##### Keywords:
rho-continuity; metric projection; convex closed sets
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##### References:
 [1] E. V. Oshman, ?On the continuity of a metric projection in a Banach space,? Mat. Sb.,80, No. 2, 181-194 (1969). [2] E. V. Oshman, ?The continuity of a metric projection and geometric properties of the unit sphere in a Banach space,? Doctoral Dissertation, Ural Univ., Sverdlovsk (1970). · Zbl 0198.45906 [3] L. P. Vlasov, ?Chebyshev sets and some of their generalizations,? Mat. Zametki,3, No. 1, 59-69 (1968). · Zbl 0155.45401 [4] E. V. Oshman and N. V. Nevesenko, ?Continuity of a multivalued metric projection in linear normed spaces,? Dokl. Akad. Nauk SSSR,223, No. 5, 1064-1066 (1975). [5] M. M. Day, Normed Linear Spaces, Springer-Verlag (1963). [6] G. Ascoli, ?Sugli spazi lineari metrici e le loro variatà lineari,? Ann. Mat. Pura Appl.,10, 33-81, 203-232 (1932). · Zbl 0003.40902 · doi:10.1007/BF02417133
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