A counterexample related to a theorem of Komjáth and Weiss

Rodrigo Carvalho; Assaf Rinot

doi:10.1016/j.topol.2025.109505

A counterexample related to a theorem of Komjáth and Weiss

Rodrigo Carvalho
, Assaf Rinot

Research output: Contribution to journal › Article › peer-review

Abstract

In a paper from 1987, Komjáth and Weiss proved that for every regular topological space X of character less than b, if X→(topω+1)_ω¹, then X→(topα)_ω¹ for all α<ω₁. In addition, assuming ⋄, they constructed a space X of size continuum, of character b, satisfying X→(topω+1)_ω¹, but not X→(topω2+1)_ω¹. Here, a counterexample space with the same characteristics is obtained outright in ZFC.

Original language	English
Article number	109505
Journal	Topology and its Applications
Volume	379
DOIs	https://doi.org/10.1016/j.topol.2025.109505
State	Published - 15 Feb 2026
Externally published	Yes

Keywords

Hajnal-Máté graphs
Partition relations of topological spaces

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2025.109505

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abstract = "In a paper from 1987, Komj{\'a}th and Weiss proved that for every regular topological space X of character less than b, if X→(topω+1)ω1, then X→(topα)ω1 for all α<ω1. In addition, assuming ⋄, they constructed a space X of size continuum, of character b, satisfying X→(topω+1)ω1, but not X→(topω2+1)ω1. Here, a counterexample space with the same characteristics is obtained outright in ZFC.",

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N2 - In a paper from 1987, Komjáth and Weiss proved that for every regular topological space X of character less than b, if X→(topω+1)ω1, then X→(topα)ω1 for all α<ω1. In addition, assuming ⋄, they constructed a space X of size continuum, of character b, satisfying X→(topω+1)ω1, but not X→(topω2+1)ω1. Here, a counterexample space with the same characteristics is obtained outright in ZFC.

AB - In a paper from 1987, Komjáth and Weiss proved that for every regular topological space X of character less than b, if X→(topω+1)ω1, then X→(topα)ω1 for all α<ω1. In addition, assuming ⋄, they constructed a space X of size continuum, of character b, satisfying X→(topω+1)ω1, but not X→(topω2+1)ω1. Here, a counterexample space with the same characteristics is obtained outright in ZFC.

KW - Hajnal-Máté graphs

KW - Partition relations of topological spaces

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A counterexample related to a theorem of Komjáth and Weiss

Abstract

Keywords

ASJC Scopus subject areas

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