A Ramsey-type topological theorem
type: Item
instance of: scholarly article
title: A Ramsey-type topological theorem
zbMATH Open document ID: 1015.54003
DOI: 10.1016/S0166-8641(01)00287-5
author: Zoltán Szentmiklóssy
author: János Gerlits
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: Two proofs are given of the following theorem: for \(r,n\geq 2\) natural numbers if \(X\) is a monotonically normal, first countable space which is not left separated and if the \(r\)-tuples of \(X\) are coloured with \(n\) colours then there is a homogeneous convergent sequence in \(X\). Examples are given to show that the hypotheses cannot be relaxed significantly.
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54D15
zbMATH DE Number: 1879130
zbMATH Keywords: homogeneous convergent sequence
reviewed by: David B. Gauld
MaRDI profile type: Publication
cites work: Q3220578
cites work: Q4150804
cites work: Combinatorial set theory: Partition relations for cardinals
cites work: Left Separated Spaces With Point-Countable Bases
cites work: Monotonically Normal Spaces
cites work: Some combinatorial problems concerning uncountable cardinals
description: scientific article; zbMATH DE number 1879130