Densely Two-Valued Metric Projections in Uniformly Convex Banach Spaces

[Zhivkov N. V.; Живков Н. В.]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 G set in the induced topology. 1991 Mathematics Subject Classification. Primary 41A65, 54E52. Secondary 46B20.Research partially supported by the National Foundation for Scientific Research at the Bulgarian Ministry of Science and Education