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Eurasian Mathematical Journal, 2015, том 6, номер 4, страницы 7–18
(Mi emj206)
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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
On finite-dimensional Banach spaces in which suns are connected
A. R. Alimov Department of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, 1 Leninskie gory, Moscow 119991 Russia
Аннотация:
The present paper extends and refines some results on the connectedness of suns in finite-dimensional normed linear spaces. In particular, a sun in a finite-dimensional $(BM)$-space is shown to be monotone path-connected and having a continuous multiplicative (additive) $\varepsilon$-selection from the operator of nearly best approximation for any $\varepsilon>0$. New properties of $(BM)$-space are put forward.
Ключевые слова и фразы:
sun, strict sun, bounded connectedness, $(BM)$-space, contractibility, nearly best approximation, $\varepsilon$-selection, Menger connectedness, monotone path-connectedness.
Поступила в редакцию: 06.09.2015
Образец цитирования:
A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj206 https://www.mathnet.ru/rus/emj/v6/i4/p7
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Страница аннотации: | 281 | PDF полного текста: | 72 | Список литературы: | 46 |
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