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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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2017
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/402 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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 \(A\in \mathfrak{F}\). |
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