An algebraic proof of van der Waerden's theorem
type: Item
instance of: scholarly article
title: An algebraic proof of van der Waerden's theorem
zbMATH Open document ID: 0704.22004
author: V. Bergelson
author: Hillel Furstenberg
author: Neil Hindman
author: Yitzhak Katznelson
published in: L'Enseignement Mathématique. 2e Série
publication date: 1989-01-01T00:00:00Z
review text: B. van der Waerden's theorem (of 1927) states that, if the natural numbers \({\mathbb{N}}\) are partitioned into finitely many subsets, then one of the subsets contains arbitrarily long arithmetic progressions. The present proof uses algebraic and topological properties of the compact right topological semigroup \(\beta\) \({\mathbb{N}}\), the Stone-Čech compactification of \({\mathbb{N}}\).
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 11B25
Mathematics Subject Classification ID: 11B05
zbMATH DE Number: 4154755
zbMATH Keywords: arithmetic progressions
zbMATH Keywords: compact right topological semigroup
zbMATH Keywords: Stone- Čech compactification
reviewed by: Paul Milnes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4154755