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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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Інститут прикладної математики і механіки НАН України
2015
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/154258 |
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irk-123456789-1542582019-06-16T01:27:15Z Ultrafilters on G-spaces Petrenko, O.V. Protasov, I.V. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/154258 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Petrenko, O.V. Protasov, I.V. |
| spellingShingle |
Petrenko, O.V. Protasov, I.V. Ultrafilters on G-spaces Algebra and Discrete Mathematics |
| author_facet |
Petrenko, O.V. Protasov, I.V. |
| author_sort |
Petrenko, O.V. |
| title |
Ultrafilters on G-spaces |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT petrenkoov ultrafiltersongspaces AT protasoviv ultrafiltersongspaces |
| first_indexed |
2023-05-20T17:43:57Z |
| last_indexed |
2023-05-20T17:43:57Z |
| _version_ |
1796153945493602304 |