Cite this article as:
Alimov A. R. Mazur Spaces and 4.3-intersection Property of (BM)-spaces. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2016, vol. 16, iss. 2, pp. 133-137. DOI: https://doi.org/10.18500/1816-9791-2016-16-2-133-137
Mazur Spaces and 4.3-intersection Property of (BM)-spaces
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).
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