Ultrafilters on G-spaces
For a discrete group G and a discrete G-space X, we identify the Stone-Cech compactifications βG and βX with the sets of all ultrafilters on G and X, and apply the natural action of βG on βX to characterize large, thick, thin, sparse and scattered subsets of X. We use G-invariant partitions and colo...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154258 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Ultrafilters on G-spaces / O.V. Petrenko, I.V. Protasov // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 254–269. — Бібліогр.: 28 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | For a discrete group G and a discrete G-space X, we identify the Stone-Cech compactifications βG and βX with the sets of all ultrafilters on G and X, and apply the natural action of βG on βX to characterize large, thick, thin, sparse and scattered subsets of X. We use G-invariant partitions and colorings to define G-selective and G-Ramsey ultrafilters on X. We show that, in contrast to the set-theoretical case, these two classes of ultrafilters are distinct. We consider also universally thin ultrafilters on ω, the T-points, and study interrelations between these ultrafilters and some classical ultrafilters on ω.
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| ISSN: | 1726-3255 |