On free vector balleans

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 coa...

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Date:2019
Main Authors: Protasov, Igor, Protasova, Ksenia
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2019
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1351
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-1351
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spelling admjournalluguniveduua-article-13512019-04-09T04:50:51Z On free vector balleans Protasov, Igor Protasova, Ksenia coarse structure, ballean, vector ballean, free vector ballean 46A17, 54E35 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 \((X, \mathcal{E})\). Lugansk National Taras Shevchenko University 2019-03-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1351 Algebra and Discrete Mathematics; Vol 27, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1351/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1351/506 Copyright (c) 2019 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2019-04-09T04:50:51Z
collection OJS
language English
topic coarse structure
ballean
vector ballean
free vector ballean
46A17
54E35
spellingShingle coarse structure
ballean
vector ballean
free vector ballean
46A17
54E35
Protasov, Igor
Protasova, Ksenia
On free vector balleans
topic_facet coarse structure
ballean
vector ballean
free vector ballean
46A17
54E35
format Article
author Protasov, Igor
Protasova, Ksenia
author_facet Protasov, Igor
Protasova, Ksenia
author_sort Protasov, Igor
title On free vector balleans
title_short On free vector balleans
title_full On free vector balleans
title_fullStr On free vector balleans
title_full_unstemmed On free vector balleans
title_sort on free vector balleans
description 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 \((X, \mathcal{E})\).
publisher Lugansk National Taras Shevchenko University
publishDate 2019
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1351
work_keys_str_mv AT protasovigor onfreevectorballeans
AT protasovaksenia onfreevectorballeans
first_indexed 2025-12-02T15:34:42Z
last_indexed 2025-12-02T15:34:42Z
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