Ultrafilters on G-spaces

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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Бібліографічні деталі
Дата:2015
Автори: Petrenko, O.V., Protasov, I.V.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2015
Назва видання:Algebra and Discrete Mathematics
Онлайн доступ:http://dspace.nbuv.gov.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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling 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
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