This article is cited in 1 paper

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.

UDC: 517.982.256

Received: 10.10.2017

DOI: 10.4213/mzm11824

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

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