Uniform ball structures
A ball structure is a triple B = (X, P, B), where X, P are nonempty sets and, for all x ∈ X, α ∈ P, B(x, α) is a subset of X, x ∈ B(x, α), which is called a ball of radius α around x. We introduce the class of uniform ball structures as an asymptotic counterpart of the class of uniform topologica...
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| Дата: | 2003 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2003
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155282 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Uniform ball structures / I.V. Protasov // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 93–102. — Бібліогр.: 2 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-155282 |
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irk-123456789-1552822019-06-17T01:30:36Z Uniform ball structures Protasov, I.V. A ball structure is a triple B = (X, P, B), where X, P are nonempty sets and, for all x ∈ X, α ∈ P, B(x, α) is a subset of X, x ∈ B(x, α), which is called a ball of radius α 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. 2003 Article Uniform ball structures / I.V. Protasov // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 93–102. — Бібліогр.: 2 назв. — англ. 1726-3255 2001 Mathematics Subject Classification: 03E99, 54A05, 54E15. http://dspace.nbuv.gov.ua/handle/123456789/155282 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A ball structure is a triple B = (X, P, B), where
X, P are nonempty sets and, for all x ∈ X, α ∈ P, B(x, α) is a subset of X, x ∈ B(x, α), which is called a ball of radius α 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. |
| format |
Article |
| author |
Protasov, I.V. |
| spellingShingle |
Protasov, I.V. Uniform ball structures Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155282 |
| citation_txt |
Uniform ball structures / I.V. Protasov // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 93–102. — Бібліогр.: 2 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT protasoviv uniformballstructures |
| first_indexed |
2023-05-20T17:45:41Z |
| last_indexed |
2023-05-20T17:45:41Z |
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1796154015747145728 |