Geodesic
Mazur spaces and 4.3-intersection property of $(BM)$-spaces
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 2, pp. 133-137

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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). 
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     author = {A. R. Alimov},
     title = {Mazur spaces and 4.3-intersection property of $(BM)$-spaces},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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A. R. Alimov. Mazur spaces and 4.3-intersection property of $(BM)$-spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 2, pp. 133-137. http://geodesic.mathdoc.fr/item/ISU_2016_16_2_a1/