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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| Date: | 2017 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2017
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/402 |
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| Journal Title: | Algebra and Discrete Mathematics |
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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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2017-07-02T21:59:43Z |
| collection |
OJS |
| language |
English |
| topic |
\(G\)-space recurrent subset ultrafilters Stone-\(\check{C}\)ech compactification 37A05 22A15 03E05 |
| 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 |
| topic_facet |
\(G\)-space recurrent subset ultrafilters Stone-\(\check{C}\)ech compactification 37A05 22A15 03E05 |
| format |
Article |
| author |
Protasov, Igor V. Protasova, Ksenia D. |
| author_facet |
Protasov, Igor V. Protasova, Ksenia D. |
| author_sort |
Protasov, Igor V. |
| title |
On recurrence in \(G\)-spaces |
| title_short |
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_sort |
on recurrence in \(g\)-spaces |
| 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 \(A\in \mathfrak{F}\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2017 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/402 |
| work_keys_str_mv |
AT protasovigorv onrecurrenceingspaces AT protasovakseniad onrecurrenceingspaces |
| first_indexed |
2025-12-02T15:31:37Z |
| last_indexed |
2025-12-02T15:31:37Z |
| _version_ |
1850412223947603968 |