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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2016, Volume 16, Issue 2, Pages 133–137 (Mi isu628)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Mazur spaces and 4.3-intersection property of $(BM)$-spaces

A. R. Alimov

Moscow State University, Vorob’evy gory, 119899, Moscow, Russia

Abstract: The paper puts forward some combinatorial and geometric properties of finite-dimensional $(BM)$-spaces. A remarkable property of such spaces is that in these spaces one succeeds in giving an answer to some long-standing problems of geometric approximation theory, and in particular, to the question on the existence of continuous $\varepsilon$-selections on suns (Kolmogorov sets) for all $\varepsilon>0$. A finite-dimensional polyhedral $(BM)$-space is shown to be a Mazur space, satisfies the 4.3-intersection property, and its unit ball is proved to be a generating set (in the sense of Polovinkin, Balashov, and Ivanov).

Key words: $(BM)$-space, 4.3-intersection property, Mazur space, Mazur set, zonotope, generating set.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00295_а
This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00295).


DOI: https://doi.org/10.18500/1816-9791-2016-16-2-133-137

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Bibliographic databases:

Document Type: Article
UDC: 517.982.252+517.982.256

Citation: A. R. Alimov, “Mazur spaces and 4.3-intersection property of $(BM)$-spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 16:2 (2016), 133–137

Citation in format AMSBIB
\Bibitem{Ali16}
\by A.~R.~Alimov
\paper Mazur spaces and 4.3-intersection property of $(BM)$-spaces
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2016
\vol 16
\issue 2
\pages 133--137
\mathnet{http://mi.mathnet.ru/isu628}
\crossref{https://doi.org/10.18500/1816-9791-2016-16-2-133-137}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3522905}
\elib{http://elibrary.ru/item.asp?id=26254370}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. R. Alimov, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Sb. Math., 208:7 (2017), 915–928  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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