The relationships among many notions of largeness for subsets of a semigroup
type: Item
instance of: scholarly article
title: The relationships among many notions of largeness for subsets of a semigroup
zbMATH Open document ID: 1426.22002
author: Neil Hindman
author: Lakeshia Legette Jones
author: D. Strauss
published in: Semigroup Forum
publication date: 2019-07-16T00:00:00Z
review text: A set \(A\subset \mathbb N\) is called \textit{thick} if it contains arbitrarily long integer intervals. The set \(A\) is \textit{syndetic} if it has bounded gaps; it is called \textit{an \(AP\)-set} if it contains arbitrarily long arithmetic progressions. The authors define analogues of these concepts for an abitrary semigroup \(S\) together with quite a few other notions which somehow embody the idea of a large subset of \(S\). They also consider \(S\) with the discrete topology and study the introduced notions in the context of \(\beta S\) providing, among other things, some combinatorial characterizations as well as the implications and counterexamples to decribe relationships between these large subsets of \(S\).
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 7080901
zbMATH Keywords: Ramsey theory
zbMATH Keywords: notions of size
zbMATH Keywords: Stone-Čech compactification
reviewed by: Vladimir Tkachuk
MaRDI profile type: Publication
full work available at URL: s00233-018-9944-3
OpenAlex ID: W2802350290
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DOI: 10.1007/S00233-018-9944-3
description: scientific article; zbMATH DE number 7080901