Metric Projection Dense G𝛿 Set Uniformly Convex Hausdorff Space of Sets Department of Operations Research
Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
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.