On recurrence in \(G\)-spaces

• Date: 2017
• Main Authors: Protasov, Igor V., Protasova, Ksenia D.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: \(G\)-space; recurrent subset; ultrafilters; Stone-\(\check{C}\)ech compactification; 37A05; 22A15; 03E05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/402
• Journal Title: Algebra and Discrete Mathematics

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}}...