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Matematicheskie Zametki, 2013, Volume 94, Issue 1, Pages 46–54
DOI: https://doi.org/10.4213/mzm9228 (Mi mzm9228) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On the Existence of Shortest Networks in Banach Spaces

B. B. Bednov, N. P. Strelkova

M. V. Lomonosov Moscow State University
Full-text PDF (478 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm9228
Abstract: For dual spaces, and also for $L_1$, it is proved that every system of points in such a space admits a shortest network connecting the points. An example of a Banach space is presented in which, for every $n\ge 3$, there is a system of $n$ points which cannot be connected by a shortest network.
Keywords: Banach space, networks connecting given points, shortest network.
Received: 09.06.2011
Revised: 19.11.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 1, Pages 41–48
DOI: https://doi.org/10.1134/S0001434613070043
Bibliographic databases:
Document Type: Article
UDC: 517.982.256+515.124.4
Language: Russian
Citation: B. B. Bednov, N. P. Strelkova, “On the Existence of Shortest Networks in Banach Spaces”, Mat. Zametki, 94:1 (2013), 46–54; Math. Notes, 94:1 (2013), 41–48
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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