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
Опубліковано в: :Algebra and Discrete Mathematics
Дата:2015
Автори: Petrenko, O.V., Protasov, I.V.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2015
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
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
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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