Binary coronas of balleans
A ballean \(\mathbb B\) 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 functi...
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/972 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543370123411456 |
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| author | Protasov, I. V. |
| author_facet | Protasov, I. V. |
| author_sort | Protasov, I. V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-14T07:18:11Z |
| description | A ballean \(\mathbb B\) 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 \(\mathbb B\). 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 \(\breve{C}\)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. |
| first_indexed | 2026-02-08T07:58:14Z |
| format | Article |
| id | admjournalluguniveduua-article-972 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:14Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9722018-05-14T07:18:11Z Binary coronas of balleans Protasov, I. V. balleans, binary corona, binary normal ballean, projective limit, normal spanning tree, end of graph 05C25, 20F65, 54A05, 54E15 A ballean \(\mathbb B\) 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 \(\mathbb B\). 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 \(\breve{C}\)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. Lugansk National Taras Shevchenko University 2018-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/972 Algebra and Discrete Mathematics; Vol 2, No 4 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/972/501 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | balleans binary corona binary normal ballean projective limit normal spanning tree end of graph 05C25 20F65 54A05 54E15 Protasov, I. V. Binary coronas of balleans |
| title | Binary coronas of balleans |
| title_full | Binary coronas of balleans |
| title_fullStr | Binary coronas of balleans |
| title_full_unstemmed | Binary coronas of balleans |
| title_short | Binary coronas of balleans |
| title_sort | binary coronas of balleans |
| topic | balleans binary corona binary normal ballean projective limit normal spanning tree end of graph 05C25 20F65 54A05 54E15 |
| topic_facet | balleans binary corona binary normal ballean projective limit normal spanning tree end of graph 05C25 20F65 54A05 54E15 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/972 |
| work_keys_str_mv | AT protasoviv binarycoronasofballeans |