TY - JOUR
T1 - A counterexample related to a theorem of Komjáth and Weiss
AU - Carvalho, Rodrigo
AU - Rinot, Assaf
N1 - Publisher Copyright:
© 2025 The Authors.
PY - 2025
Y1 - 2025
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
UR - https://www.scopus.com/pages/publications/105010307271
U2 - 10.1016/j.topol.2025.109505
DO - 10.1016/j.topol.2025.109505
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AN - SCOPUS:105010307271
SN - 0166-8641
VL - 379
JO - Topology and its Applications
JF - Topology and its Applications
M1 - 109505
ER -