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Title: Densely Two-Valued Metric Projections in Uniformly Convex Banach Spaces
Authors: Zhivkov, N. V.
Keywords: Metric Projection
Dense G𝛿 Set
Uniformly Convex
Hausdorff Space of Sets
Department of Operations Research
Issue Date: May-1994
Publisher: Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
Citation: Preprint
Series/Report no.: 1994;1
Abstract: For every uniformly convex Banach space X with dim X ≥ 2 there is a residual set U in the Hausdorff metric space B(X) of hounded and closed sets in X such that a metric projection generated by a set from U is two-valued and upper semicontinuous on a dense and everywhere continual subset of X. For any two closed and separated subsets M1 and M2 of X the points on the equidistant hypersurface which have best approximations both in M1 and M2 form a dense G𝛿 set in the induced topology. 1991 Mathematics Subject Classification. Primary 41A65, 54E52. Secondary 46B20.
Description: [Zhivkov N. V.; Живков Н. В.]
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