Uniform ball structures
A ball structure is a triple \(\mathbb B=(X,P,B)\), where \(X,P\) are nonempty sets and, for all \(x\in X\), \(\alpha \in P\), \(B(x,\alpha )\) is a subset of \(X, x\in B(x,\alpha )\), which is called a ball of radius \(\alpha \) around \(x\). We introduce the class of uniform ball structures as an...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1145 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-11452018-05-13T06:43:21Z Uniform ball structures Protasov, I. V. ball structure, metrizability 03E99, 54A05, 54E15 A ball structure is a triple \(\mathbb B=(X,P,B)\), where \(X,P\) are nonempty sets and, for all \(x\in X\), \(\alpha \in P\), \(B(x,\alpha )\) is a subset of \(X, x\in B(x,\alpha )\), which is called a ball of radius \(\alpha \) around \(x\). We introduce the class of uniform ball structures as an asymptotic counterpart of the class of uniform topological spaces. We show that every uniform ball structure can be approximated by metrizable ball structures. We also define two types of ball structures closed to being metrizable, and describe the extremal elements in the classes of ball structures with fixed support \(X\). Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1145 Algebra and Discrete Mathematics; Vol 2, No 1 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1145/637 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
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OJS |
| language |
English |
| topic |
ball structure metrizability 03E99 54A05 54E15 |
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ball structure metrizability 03E99 54A05 54E15 Protasov, I. V. Uniform ball structures |
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ball structure metrizability 03E99 54A05 54E15 |
| format |
Article |
| author |
Protasov, I. V. |
| author_facet |
Protasov, I. V. |
| author_sort |
Protasov, I. V. |
| title |
Uniform ball structures |
| title_short |
Uniform ball structures |
| title_full |
Uniform ball structures |
| title_fullStr |
Uniform ball structures |
| title_full_unstemmed |
Uniform ball structures |
| title_sort |
uniform ball structures |
| description |
A ball structure is a triple \(\mathbb B=(X,P,B)\), where \(X,P\) are nonempty sets and, for all \(x\in X\), \(\alpha \in P\), \(B(x,\alpha )\) is a subset of \(X, x\in B(x,\alpha )\), which is called a ball of radius \(\alpha \) around \(x\). We introduce the class of uniform ball structures as an asymptotic counterpart of the class of uniform topological spaces. We show that every uniform ball structure can be approximated by metrizable ball structures. We also define two types of ball structures closed to being metrizable, and describe the extremal elements in the classes of ball structures with fixed support \(X\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1145 |
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AT protasoviv uniformballstructures |
| first_indexed |
2024-04-12T06:25:08Z |
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2024-04-12T06:25:08Z |
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1796109229002588160 |