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Mat. Zametki, 2018, Volume 104, Issue 5, Pages 694–699 (Mi mz11824)  

On Selections from the Best $n$-Nets

Yu. Yu. Druzhinin

State-Funded Educational Institution Lycée 1158, Moscow, 117648 Russia

Abstract: The discontinuity of any selection from a best $n$-net for $n\ge 2$ in an arbitrary not strictly convex Banach space is proved. It is also proved that there is no Lipschitz selection on an arbitrary Banach space of dimension at least 2 whose unit sphere contains an attainable point of smoothness.

Keywords: Banach space, selection, best $n$-net, Chebyshev center.

DOI: https://doi.org/10.4213/mzm11824

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English version:
Mathematical Notes, 2018, 104:5, 678–682

Bibliographic databases:

Document Type: Article
UDC: 517.982.256
Received: 10.10.2017

Citation: Yu. Yu. Druzhinin, “On Selections from the Best $n$-Nets”, Mat. Zametki, 104:5 (2018), 694–699; Math. Notes, 104:5 (2018), 678–682

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