On the subset combinatorics of \(G\)-spaces
Let \(G\) be a group and let \(X\) be a transitive \(G\)-space. We classify the subsets of \(X\) with respect to a translation invariant ideal \({J}\) in the Boolean algebra of all subsets of \(X\), introduce and apply the relative combinatorical derivations of subsets of \(X\). Using the standard a...
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| Date: | 2018 |
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| 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/1026 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-10262018-04-26T01:41:11Z On the subset combinatorics of \(G\)-spaces Protasov, Igor Slobodianiuk, Sergii \(G\)-space, relative combinatorial derivation, Stone-\(\check{C}\)ech compactification, ultracompanion, sparse and scattered subsets 20F69, 22A15, 54D35 Let \(G\) be a group and let \(X\) be a transitive \(G\)-space. We classify the subsets of \(X\) with respect to a translation invariant ideal \({J}\) in the Boolean algebra of all subsets of \(X\), introduce and apply the relative combinatorical derivations of subsets of \(X\). Using the standard action of \(G\) on the Stone-\(\check{C}\)ech compactification \(\beta X\) of the discrete space \(X\), we characterize the points \(p\in\beta X\) isolated in \(Gp\) and describe a size of a subset of \(X\) in terms of its ultracompanions in \(\beta X\). We introduce and characterize scattered and sparse subsets of \(X\) from different points of view. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1026 Algebra and Discrete Mathematics; Vol 17, No 1 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1026/550 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-04-26T01:41:11Z |
| collection |
OJS |
| language |
English |
| topic |
\(G\)-space relative combinatorial derivation Stone-\(\check{C}\)ech compactification ultracompanion sparse and scattered subsets 20F69 22A15 54D35 |
| spellingShingle |
\(G\)-space relative combinatorial derivation Stone-\(\check{C}\)ech compactification ultracompanion sparse and scattered subsets 20F69 22A15 54D35 Protasov, Igor Slobodianiuk, Sergii On the subset combinatorics of \(G\)-spaces |
| topic_facet |
\(G\)-space relative combinatorial derivation Stone-\(\check{C}\)ech compactification ultracompanion sparse and scattered subsets 20F69 22A15 54D35 |
| format |
Article |
| author |
Protasov, Igor Slobodianiuk, Sergii |
| author_facet |
Protasov, Igor Slobodianiuk, Sergii |
| author_sort |
Protasov, Igor |
| title |
On the subset combinatorics of \(G\)-spaces |
| title_short |
On the subset combinatorics of \(G\)-spaces |
| title_full |
On the subset combinatorics of \(G\)-spaces |
| title_fullStr |
On the subset combinatorics of \(G\)-spaces |
| title_full_unstemmed |
On the subset combinatorics of \(G\)-spaces |
| title_sort |
on the subset combinatorics of \(g\)-spaces |
| description |
Let \(G\) be a group and let \(X\) be a transitive \(G\)-space. We classify the subsets of \(X\) with respect to a translation invariant ideal \({J}\) in the Boolean algebra of all subsets of \(X\), introduce and apply the relative combinatorical derivations of subsets of \(X\). Using the standard action of \(G\) on the Stone-\(\check{C}\)ech compactification \(\beta X\) of the discrete space \(X\), we characterize the points \(p\in\beta X\) isolated in \(Gp\) and describe a size of a subset of \(X\) in terms of its ultracompanions in \(\beta X\). We introduce and characterize scattered and sparse subsets of \(X\) from different points of view. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1026 |
| work_keys_str_mv |
AT protasovigor onthesubsetcombinatoricsofgspaces AT slobodianiuksergii onthesubsetcombinatoricsofgspaces |
| first_indexed |
2025-07-17T10:33:12Z |
| last_indexed |
2025-07-17T10:33:12Z |
| _version_ |
1837889898661543936 |