Binary coronas of balleans
A ballean B is a set X endowed with some family of subsets of X which are called the balls. We postulate the properties of the family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. Using slow oscillating functions from X to {0,...
Збережено в:
| 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/123456789/155724 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Binary coronas of balleans / I.V. Protasov // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 50–65. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | A ballean B is a set X endowed with some family
of subsets of X which are called the balls. We postulate the properties of the family of balls in such a way that a ballean can be
considered as an asymptotic counterpart of a uniform topological
space. Using slow oscillating functions from X to {0, 1}, we define
a zero-dimensional compact space which is called a binary corona
of B. We define a class of binary normal ballean and, for every ballean from this class, give an intrinsic characterization of its binary
corona. The class of binary normal balleans contains all balleans
of graph. We show that a ballean of graph is a projective limit of
some sequence of C˘ech-Stone compactifications of discrete spaces.
The obtained results witness that a binary corona of balleans can
be interpreted as a "generalized space of ends" of ballean. |
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