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...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1026 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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