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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2003 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2003
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155285 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Protasov, I.V. 2019-06-16T15:32:41Z 2019-06-16T15:32:41Z 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/123456789/155285 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Uniform ball structures |
| spellingShingle |
Uniform ball structures Protasov, I.V. |
| 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 |
| author |
Protasov, I.V. |
| author_facet |
Protasov, I.V. |
| publishDate |
2003 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155285 |
| citation_txt |
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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AT protasoviv uniformballstructures |
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2025-12-01T15:28:32Z |
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2025-12-01T15:28:32Z |
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1850860594807177216 |