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Algebra and Discrete Mathematics, 2006, выпуск 4, страницы 81–92
(Mi adm281)
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RESEARCH ARTICLE
Pseudodiscrete balleans
O. I. Protasova Department of Cybernetics, Kyiv National University, Volodimirska 64, Kiev 01033, Ukraine
Аннотация:
A ballean $\mathcal{B}$ is a set $X$ endowed with some family of subsets of $X$ which are called the balls. The properties of the balls are postulated in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. A ballean is called pseudodiscrete if “almost all” balls of every pregiven radius are singletons. We give a filter characterization of pseudodiscrete balleans and their classification up to quasi-asymorphisms. It is proved that a ballean is pseudodiscrete if and only if every real function defined on its support is slowly oscillating. We show that the class of irresolvable balleans are tightly connected with the class of pseudodiscrete balleans.
Ключевые слова:
ballean, pseudodiscrete ballean, pseudobounded ballean, slowly oscillating function, irresolvable ballean, asymorphism, quasi-asymorphism.
Поступила в редакцию: 11.05.2003 Исправленный вариант: 29.03.2007
Образец цитирования:
O. I. Protasova, “Pseudodiscrete balleans”, Algebra Discrete Math., 2006, no. 4, 81–92
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm281 https://www.mathnet.ru/rus/adm/y2006/i4/p81
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