Hajnal, András; Juhász, István; Weiss, William Partitioning the pairs and triples of topological spaces. (English) Zbl 0703.04001 Topology Appl. 35, No. 2-3, 177-184 (1990). 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. Reviewer: K.P.Hart Cited in 4 Documents MSC: 03E05 Other combinatorial set theory 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54A35 Consistency and independence results in general topology Keywords:partition calculus; square; topological partition theory PDFBibTeX XMLCite \textit{A. Hajnal} et al., Topology Appl. 35, No. 2--3, 177--184 (1990; Zbl 0703.04001) Full Text: DOI References: [1] Devlin, K., Constructibility (1984), Springer: Springer Berlin · Zbl 0542.03029 [2] Erdös, P.; Hajnal, A.; Máte, A.; Rado, R., Combinatorial Set Theory: Partition Relations for Cardinals (1984), North-Holland: North-Holland Amsterdam · Zbl 0573.03019 [3] Hajnal, A.; Juhász, I., A consistency result concerning hereditarily α-separable spaces, Indag. Math., 35, 307-310 (1973) · Zbl 0292.54006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.