Partitioning the pairs and triples of topological spaces
type: Item
instance of: scholarly article
title: Partitioning the pairs and triples of topological spaces
zbMATH Open document ID: 0703.04001
DOI: 10.1016/0166-8641(90)90103-9
author: István Juhász
author: Andras Hajnal
author: William A. R. Weiss
published in: Topology and its Applications
publication date: 1990-01-01T00:00:00Z
review text: This paper contains contributions to topological partition theory. The main results are: 1. The existence, for every uncountable \(\kappa\), of a space X such that \(X\to (B_{\kappa})^ 2_{\omega}\), where \(B_{\kappa}\) is \(\kappa +1\) with the limit ordinals below \(\kappa\) removed. In fact X can be taken to be a cardinal with the order topology and if \(\kappa\) is weakly compact then \(X=\kappa^+.\) 2. For every Hausdorff space X a partition of \([X]^ 2\) into two pieces without any dense-in-itself homogeneous set. 3. Negative results about \(X\to (Y)^ n_{\omega}:\) if for every \(\kappa\) of countable cofinality both \(\kappa^{\omega}=\kappa^+\) and \(\square_{\kappa}\) hold then for every regular X the relations \(X\to (top \omega +1)^ 2_{\omega}\) and \(X\to (Y)^ 3_{\omega}\) (Y countable and nondiscrete) are false.
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54A35
zbMATH DE Number: 4152379
zbMATH Keywords: partition calculus
zbMATH Keywords: square
zbMATH Keywords: topological partition theory
reviewed by: K. P. Hart
MaRDI profile type: Publication
full work available at URL: 0166-8641(90)90103-9
OpenAlex ID: W2002000359
cites work: Q3329455
cites work: Combinatorial set theory: Partition relations for cardinals
cites work: Q4043743
cites work: Q3972757
description: scientific article; zbMATH DE number 4152379