On recurrence in \(G\)-spaces
We introduce and analyze the following general concept of recurrence. Let \(G\) be a group and let \(X\) be a G-space with the action \(G\times X\longrightarrow X\), \((g,x)\longmapsto gx\). For a family \(\mathfrak{F}\) of subset of \(X\) and \(A\in \mathfrak{F}\), we denote \(\Delta_{\mathfrak{F}}...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2017
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/402 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543061932244992 |
|---|---|
| author | Protasov, Igor V. Protasova, Ksenia D. |
| author_facet | Protasov, Igor V. Protasova, Ksenia D. |
| author_sort | Protasov, Igor V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-07-02T21:59:43Z |
| description | We introduce and analyze the following general concept of recurrence. Let \(G\) be a group and let \(X\) be a G-space with the action \(G\times X\longrightarrow X\), \((g,x)\longmapsto gx\). For a family \(\mathfrak{F}\) of subset of \(X\) and \(A\in \mathfrak{F}\), we denote \(\Delta_{\mathfrak{F}}(A)=\{g\in G: gB\subseteq A\) for some \(B\in \mathfrak{F}\), \(B\subseteq A\}\), and say that a subset \(R\) of \(G\) is \(\mathfrak{F}\)-recurrent if \(R\bigcap \Delta_{\mathfrak{F}} (A)\neq\emptyset\) for each \(A\in \mathfrak{F}\). |
| first_indexed | 2025-12-02T15:31:37Z |
| format | Article |
| id | admjournalluguniveduua-article-402 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:31:37Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-4022017-07-02T21:59:43Z On recurrence in \(G\)-spaces Protasov, Igor V. Protasova, Ksenia D. \(G\)-space, recurrent subset, ultrafilters, Stone-\(\check{C}\)ech compactification 37A05, 22A15, 03E05 We introduce and analyze the following general concept of recurrence. Let \(G\) be a group and let \(X\) be a G-space with the action \(G\times X\longrightarrow X\), \((g,x)\longmapsto gx\). For a family \(\mathfrak{F}\) of subset of \(X\) and \(A\in \mathfrak{F}\), we denote \(\Delta_{\mathfrak{F}}(A)=\{g\in G: gB\subseteq A\) for some \(B\in \mathfrak{F}\), \(B\subseteq A\}\), and say that a subset \(R\) of \(G\) is \(\mathfrak{F}\)-recurrent if \(R\bigcap \Delta_{\mathfrak{F}} (A)\neq\emptyset\) for each \(A\in \mathfrak{F}\). Lugansk National Taras Shevchenko University 2017-07-03 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/402 Algebra and Discrete Mathematics; Vol 23, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/402/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/402/169 Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | \(G\)-space recurrent subset ultrafilters Stone-\(\check{C}\)ech compactification 37A05 22A15 03E05 Protasov, Igor V. Protasova, Ksenia D. On recurrence in \(G\)-spaces |
| title | On recurrence in \(G\)-spaces |
| title_full | On recurrence in \(G\)-spaces |
| title_fullStr | On recurrence in \(G\)-spaces |
| title_full_unstemmed | On recurrence in \(G\)-spaces |
| title_short | On recurrence in \(G\)-spaces |
| title_sort | on recurrence in \(g\)-spaces |
| topic | \(G\)-space recurrent subset ultrafilters Stone-\(\check{C}\)ech compactification 37A05 22A15 03E05 |
| topic_facet | \(G\)-space recurrent subset ultrafilters Stone-\(\check{C}\)ech compactification 37A05 22A15 03E05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/402 |
| work_keys_str_mv | AT protasovigorv onrecurrenceingspaces AT protasovakseniad onrecurrenceingspaces |