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.
