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Matematicheskie Zametki, 2018, Volume 104, Issue 5, Pages 694–699
DOI: https://doi.org/10.4213/mzm11824 (Mi mzm11824) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Selections from the Best $n$-Nets

Yu. Yu. Druzhinin

State-Funded Educational Institution Lycée 1158, Moscow, 117648 Russia
Full-text PDF (452 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm11824
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.
Received: 10.10.2017
English version:
Mathematical Notes, 2018, Volume 104, Issue 5, Pages 678–682
DOI: https://doi.org/10.1134/S000143461811007X
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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