## 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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## Bibliographic Information

- © Copyright 1995 American Mathematical Society
- 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