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...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
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| 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/123456789/155285 |
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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| Резюме: | 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.
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| ISSN: | 1726-3255 |