Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Alimov A. R. Mazur Spaces and 4.3-intersection Property of (BM)-spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 133-137. DOI: 10.18500/1816-9791-2016-16-2-133-137, EDN: WCNQGP

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.06.2016
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.982.252+517.982.256
DOI: 
10.18500/1816-9791-2016-16-2-133-137
EDN: 
WCNQGP

Mazur Spaces and 4.3-intersection Property of (BM)-spaces

Autors: 
Alimov A. R., Lomonosov Moscow State University
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 ε-selections on suns (Kolmogorov sets) for all ε > 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
References: 
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Received: 
20.01.2016
Accepted: 
29.05.2016
Published: 
30.06.2016
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