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Algebra and Discrete Mathematics, 2019, том 27, выпуск 1, страницы 70–74
(Mi adm693)
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RESEARCH ARTICLE
On free vector balleans
Igor Protasov, Ksenia Protasova Department of Computer Science and Cybernetics, Kyiv University, Volodymyrska 64, 01033, Kyiv, Ukraine
Аннотация:
A vector balleans is a vector space over $\mathbb{R}$ endowed with a coarse structure in such a way that the vector operations are coarse mappings. We prove that, for every ballean $(X, \mathcal{E})$, there exists the unique free vector ballean $\mathbb{V}(X, \mathcal{E})$ and describe the coarse structure of $\mathbb{V}(X, \mathcal{E})$. It is shown that normality of $\mathbb{V}(X, \mathcal{E})$ is equivalent to metrizability of $(X, \mathcal{E})$.
Ключевые слова:
coarse structure, ballean, vector ballean, free vector ballean.
Поступила в редакцию: 10.03.2019
Образец цитирования:
Igor Protasov, Ksenia Protasova, “On free vector balleans”, Algebra Discrete Math., 27:1 (2019), 70–74
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm693 https://www.mathnet.ru/rus/adm/v27/i1/p70
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Статистика просмотров: |
Страница аннотации: | 45 | PDF полного текста: | 18 | Список литературы: | 13 |
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