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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
DOI: https://doi.org/10.1090/S0002-9939-1995-1273531-0
MathSciNet review: 1273531
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Abstract: In every strictly convexifiable Banach space X with $ \dim X \geq 2$ there exists a dense $ {G_\delta }$ set of compacta $ \mathcal{A}$ 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 $ \mathcal{A}$ are densely multivalued.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1273531-0
Keywords: dense $ {G_\delta }$, metric projection, antiprojection, ambiguous locus
Article copyright: © Copyright 1995 American Mathematical Society

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