Compacta with dense ambiguous loci of metric projections and antiprojections

Zhivkov, N. V.

doi:10.1090/S0002-9939-1995-1273531-0

Compacta with dense ambiguous loci of metric projections and antiprojections
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by N. V. Zhivkov

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

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

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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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