Compacta with dense ambiguous loci of metric projections and antiprojections

Author:
N. V. Zhivkov

Journal:
Proc. Amer. Math. Soc. **123** (1995), 3403-3411

MSC:
Primary 41A65; Secondary 46B20, 54E52

MathSciNet review:
1273531

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Abstract | References | Similar Articles | Additional Information

Abstract: In every strictly convexifiable Banach space *X* with there exists a dense set of compacta in the Hausdorff set topology such that with respect to an arbitrary equivalent strictly convex norm in *X* both the metric projection and the metric antiprojection generated by any member of are densely multivalued.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1273531-0

Keywords:
dense ,
metric projection,
antiprojection,
ambiguous locus

Article copyright:
© Copyright 1995
American Mathematical Society