On the subset combinatorics of \(G\)-spaces
Let \(G\) be a group and let \(X\) be a transitive \(G\)-space. We classify the subsets of \(X\) with respect to a translation invariant ideal \({J}\) in the Boolean algebra of all subsets of \(X\), introduce and apply the relative combinatorical derivations of subsets of \(X\). Using the standard a...
Збережено в:
| Дата: | 2018 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1026 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | Let \(G\) be a group and let \(X\) be a transitive \(G\)-space. We classify the subsets of \(X\) with respect to a translation invariant ideal \({J}\) in the Boolean algebra of all subsets of \(X\), introduce and apply the relative combinatorical derivations of subsets of \(X\). Using the standard action of \(G\) on the Stone-\(\check{C}\)ech compactification \(\beta X\) of the discrete space \(X\), we characterize the points \(p\in\beta X\) isolated in \(Gp\) and describe a size of a subset of \(X\) in terms of its ultracompanions in \(\beta X\). We introduce and characterize scattered and sparse subsets of \(X\) from different points of view. |
|---|