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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| Видавець: | Lugansk National Taras Shevchenko University |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2019
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1351 |
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Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-1351 |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| 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 |
2024-04-12T06:25:10Z |
| last_indexed |
2024-04-12T06:25:10Z |
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1796109230101495808 |