Ultrafilters on \(G\)-spaces

• Date: 2015
• Main Authors: Petrenko, O. V., Protasov, I. V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2015
• Subjects: \(G\)-space; ultrafilters; ultracompanion; \(G\)-selective ultrafilter; \(G\)-Ramsey ultrafilter; \(T\)-point; ballean; asymorphism; 05D10; 22A15; 54H20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/69
• Journal Title: Algebra and Discrete Mathematics

For a discrete group \(G\) and a discrete \(G\)-space \(X\), we identify the Stone-Cech compactifications \(\beta G\) and \(\beta X\) with the sets of all ultrafilters on \(G\) and \(X\), and apply the natural action of \(\beta G\) on \(\beta X\) to characterize large, thick, thin, sparse and scatte...