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Sbornik: Mathematics, 2014, Volume 205, Issue 8, Pages 1160–1200
DOI: https://doi.org/10.1070/SM2014v205n08ABEH004414 (Mi sm8316) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Covering sets in $\mathbb{R}^m$

V. P. Filimonov

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
English version PDF (665 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM2014v205n08ABEH004414
Abstract: The paper investigates questions related to Borsuk's classical problem of partitioning a set in Euclidean space into subsets of smaller diameter, as well as to the well-known Nelson-Erdős-Hadwiger problem on the chromatic number of a Euclidean space.
The results of the work are obtained using combinatorial and geometric methods alike. A new approach to the investigation of such problems is suggested; it leads to a collection of results which significantly improve all results known so far.
Bibliography: 58 titles.
Keywords: chromatic number, Borsuk's problem, diameter of a set, covering of a plane set, universal covering sets and systems.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00759-а
Received: 16.12.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 8, Pages 95–138
DOI: https://doi.org/10.4213/sm8316
Bibliographic databases:
Document Type: Article
UDC: 514.174
MSC: 52C17
Language: English
Original paper language: Russian
Citation: V. P. Filimonov, “Covering sets in $\mathbb{R}^m$”, Mat. Sb., 205:8 (2014), 95–138; Sb. Math., 205:8 (2014), 1160–1200
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2014v205n08ABEH004414
  • https://www.mathnet.ru/eng/sm/v205/i8/p95
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:427
    Russian version PDF:184
    English version PDF:20
    References:55
    First page:30
     
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