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 cla...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2003 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2003
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| Онлайн доступ: | https://nasplib.isofts.kiev.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706199380623360 |
|---|---|
| author | Protasov, I.V. |
| author_facet | Protasov, I.V. |
| citation_txt | Uniform ball structures / I.V. Protasov // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 93–102. — Бібліогр.: 2 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T16:58:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155282 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:58:07Z |
| publishDate | 2003 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Protasov, I.V. 2019-06-16T15:31:30Z 2019-06-16T15:31:30Z 2003 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. https://nasplib.isofts.kiev.ua/handle/123456789/155282 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Uniform ball structures Article published earlier |
| spellingShingle | Uniform ball structures Protasov, I.V. |
| title | Uniform ball structures |
| title_full | Uniform ball structures |
| title_fullStr | Uniform ball structures |
| title_full_unstemmed | Uniform ball structures |
| title_short | Uniform ball structures |
| title_sort | uniform ball structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155282 |
| work_keys_str_mv | AT protasoviv uniformballstructures |