Continuity of the Metric Projection and Local Solar Properties of Sets
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The paper is concerned with local approximative and geometric properties of sets, with particular emphasis on strict solarity of such sets under certain constraints on the continuity of metric projections. A partial answer is given to the question due to B. Brosowski and F. Deutsch as to when the class of strict protosuns (Kolmogorov sets) coincides with the class of sets with outer radially continuous metric projection. The lower semi-continuous metric projection with monotone path-connected values is shown to have a continuous selection. A number of related results is obtained.
KeywordsChebyshev set Sun Strict sun Radial continuity Bounded solarity Selection of the metric projection operator Best approximation Near-best approximation
Mathematics Subject Classification (2010)41A65 54C65
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The author is grateful to the referees for suggestions which have removed obscurities.
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