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...
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| 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| id |
nasplib_isofts_kiev_ua-123456789-154258 |
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Petrenko, O.V. Protasov, I.V. 2019-06-15T11:57:48Z 2019-06-15T11:57:48Z 2015 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. 1726-3255 2010 MSC:05D10, 22A15, 54H20 https://nasplib.isofts.kiev.ua/handle/123456789/154258 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Ultrafilters on G-spaces Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Ultrafilters on G-spaces |
| spellingShingle |
Ultrafilters on G-spaces Petrenko, O.V. Protasov, I.V. |
| title_short |
Ultrafilters on G-spaces |
| title_full |
Ultrafilters on G-spaces |
| title_fullStr |
Ultrafilters on G-spaces |
| title_full_unstemmed |
Ultrafilters on G-spaces |
| title_sort |
ultrafilters on g-spaces |
| author |
Petrenko, O.V. Protasov, I.V. |
| author_facet |
Petrenko, O.V. Protasov, I.V. |
| publishDate |
2015 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154258 |
| citation_txt |
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. |
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AT petrenkoov ultrafiltersongspaces AT protasoviv ultrafiltersongspaces |
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2025-12-07T13:18:51Z |
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2025-12-07T13:18:51Z |
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1850855686698696704 |