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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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154258 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862619675212382208 |
|---|---|
| author | Petrenko, O.V. Protasov, I.V. |
| author_facet | Petrenko, O.V. Protasov, I.V. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T13:18:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154258 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:18:51Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Ultrafilters on G-spaces Petrenko, O.V. Protasov, I.V. |
| title | Ultrafilters on G-spaces |
| title_full | Ultrafilters on G-spaces |
| title_fullStr | Ultrafilters on G-spaces |
| title_full_unstemmed | Ultrafilters on G-spaces |
| title_short | Ultrafilters on G-spaces |
| title_sort | ultrafilters on g-spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154258 |
| work_keys_str_mv | AT petrenkoov ultrafiltersongspaces AT protasoviv ultrafiltersongspaces |