$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 $\beta G$ and $\beta X$ with the sets of all ultrafilters on $G$ and $X$, and apply the natural action of $\beta G$ on $\beta X$ to characterize large, thick, thin, sparse and scatte...

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Datum:	2015
Hauptverfasser:	Petrenko, O. V., Protasov, I. V.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Lugansk National Taras Shevchenko University 2015
Schlagworte:	$G$-space ultrafilters ultracompanion $G$-selective ultrafilter $G$-Ramsey ultrafilter $T$-point ballean asymorphism 05D10 22A15 54H20
Online Zugang:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/69
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Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	admjournalluguniveduua-article-69
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spelling	admjournalluguniveduua-article-692015-09-28T11:22:08Z Ultrafilters on $G$-spaces Petrenko, O. V. Protasov, I. V. $G$-space, ultrafilters, ultracompanion, $G$-selective ultrafilter, $G$-Ramsey ultrafilter, $T$-point, ballean, asymorphism 05D10, 22A15, 54H20 For a discrete group $G$ and a discrete $G$-space $X$, we identify the Stone-Cech compactifications $\beta G$ and $\beta X$ with the sets of all ultrafilters on $G$ and $X$, and apply the natural action of $\beta G$ on $\beta X$ 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 $\omega$, the $T$-points, and study interrelations between these ultrafilters and some classical ultrafilters on $\omega$. Lugansk National Taras Shevchenko University 2015-09-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/69 Algebra and Discrete Mathematics; Vol 19, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/69/18 Copyright (c) 2015 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2015-09-28T11:22:08Z
collection	OJS
language	English
topic	$G$-space ultrafilters ultracompanion $G$-selective ultrafilter $G$-Ramsey ultrafilter $T$-point ballean asymorphism 05D10 22A15 54H20
spellingShingle	$G$-space ultrafilters ultracompanion $G$-selective ultrafilter $G$-Ramsey ultrafilter $T$-point ballean asymorphism 05D10 22A15 54H20 Petrenko, O. V. Protasov, I. V. Ultrafilters on $G$-spaces
topic_facet	$G$-space ultrafilters ultracompanion $G$-selective ultrafilter $G$-Ramsey ultrafilter $T$-point ballean asymorphism 05D10 22A15 54H20
format	Article
author	Petrenko, O. V. Protasov, I. V.
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
description	For a discrete group $G$ and a discrete $G$-space $X$, we identify the Stone-Cech compactifications $\beta G$ and $\beta X$ with the sets of all ultrafilters on $G$ and $X$, and apply the natural action of $\beta G$ on $\beta X$ 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 $\omega$, the $T$-points, and study interrelations between these ultrafilters and some classical ultrafilters on $\omega$.
publisher	Lugansk National Taras Shevchenko University
publishDate	2015
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/69
work_keys_str_mv	AT petrenkoov ultrafiltersongspaces AT protasoviv ultrafiltersongspaces
first_indexed	2025-12-02T15:46:28Z
last_indexed	2025-12-02T15:46:28Z
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Ultrafilters on \(G\)-spaces

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