Pseudodiscrete balleans
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...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/908 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543367710638080 |
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| author | Protasova, O. I. |
| author_facet | Protasova, O. I. |
| author_sort | Protasova, O. I. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T07:55:00Z |
| description | 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. |
| first_indexed | 2026-02-08T07:58:11Z |
| format | Article |
| id | admjournalluguniveduua-article-908 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:11Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9082018-03-21T07:55:00Z Pseudodiscrete balleans Protasova, O. I. ballean, pseudodiscrete ballean, pseudobounded ballean, slowly oscillating function, irresolvable ballean, asymorphism, quasiasymorphism 03E05, 03E75, 06A11, 54A05,54E15. 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/908 Algebra and Discrete Mathematics; Vol 5, No 4 (2006) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/908/437 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | ballean pseudodiscrete ballean pseudobounded ballean slowly oscillating function irresolvable ballean asymorphism quasiasymorphism 03E05 03E75 06A11 54A05,54E15. Protasova, O. I. Pseudodiscrete balleans |
| title | Pseudodiscrete balleans |
| title_full | Pseudodiscrete balleans |
| title_fullStr | Pseudodiscrete balleans |
| title_full_unstemmed | Pseudodiscrete balleans |
| title_short | Pseudodiscrete balleans |
| title_sort | pseudodiscrete balleans |
| topic | ballean pseudodiscrete ballean pseudobounded ballean slowly oscillating function irresolvable ballean asymorphism quasiasymorphism 03E05 03E75 06A11 54A05,54E15. |
| topic_facet | ballean pseudodiscrete ballean pseudobounded ballean slowly oscillating function irresolvable ballean asymorphism quasiasymorphism 03E05 03E75 06A11 54A05,54E15. |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/908 |
| work_keys_str_mv | AT protasovaoi pseudodiscreteballeans |