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 action of G on the Stone-ˇCech...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2014 |
| ISSN: | 1726-3255 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152346 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the subset combinatorics of G-spaces / I. Protasov, S. Slobodianiuk // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 1. — С. 98–109. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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-ˇCech compactification βX of the discrete space X, we characterize the points p ∈ βX isolated in Gp and describe a size of a subset of X in terms of its ultracompanions in βX. We introduce and characterize scattered and sparse subsets of X from different points of view.
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| ISSN: | 1726-3255 |