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Mat. Zametki, 2013, Volume 94, Issue 1, Pages 46–54 (Mi mz9228)  

This article is cited in 5 scientific papers (total in 5 papers)

On the Existence of Shortest Networks in Banach Spaces

B. B. Bednov, N. P. Strelkova

M. V. Lomonosov Moscow State University

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.

DOI: https://doi.org/10.4213/mzm9228

Full text: PDF file (478 kB)
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English version:
Mathematical Notes, 2013, 94:1, 41–48

Bibliographic databases:

UDC: 517.982.256+515.124.4
Received: 09.06.2011
Revised: 19.11.2012

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. O. Ivanov, A. E. Mel'nikova, A. A. Tuzhilin, “Stabilization of a locally minimal forest”, Sb. Math., 205:3 (2014), 387–418  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. B. B. Bednov, P. A. Borodin, “Banach spaces that realize minimal fillings”, Sb. Math., 205:4 (2014), 459–475  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. O. Ivanov, N. K. Nikolaeva, A. A. Tuzhilin, “Problema Shteinera v prostranstve Gromova–Khausdorfa: sluchai konechnykh metricheskikh prostranstv”, Tr. IMM UrO RAN, 23, no. 4, 2017, 152–161  mathnet  crossref  elib
    4. B. B. Bednov, “The length of minimal filling for a five-point metric space”, Moscow University Mathematics Bulletin, 72:6 (2017), 221–225  mathnet  crossref  mathscinet  zmath  isi  elib
    5. L. Sh. Burusheva, “Banach spaces with shortest network length depending only on pairwise distances between points”, Sb. Math., 210:3 (2019), 297–309  mathnet  crossref  crossref  elib
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