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Algebra and Discrete Mathematics, 2006, Issue 4, Pages 81–92 (Mi adm281)  

RESEARCH ARTICLE

Pseudodiscrete balleans

O. I. Protasova

Department of Cybernetics, Kyiv National University, Volodimirska 64, Kiev 01033, Ukraine
Abstract: 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.
Keywords: ballean, pseudodiscrete ballean, pseudobounded ballean, slowly oscillating function, irresolvable ballean, asymorphism, quasi-asymorphism.
Received: 11.05.2003
Revised: 29.03.2007
Bibliographic databases:
Document Type: Article
Language: English
Citation: O. I. Protasova, “Pseudodiscrete balleans”, Algebra Discrete Math., 2006, no. 4, 81–92
Citation in format AMSBIB
\Bibitem{Pro06}
\by O.~I.~Protasova
\paper Pseudodiscrete balleans
\jour Algebra Discrete Math.
\yr 2006
\issue 4
\pages 81--92
\mathnet{http://mi.mathnet.ru/adm281}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2319410}
\zmath{https://zbmath.org/?q=an:1118.54017}
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