A counterexample related to a theorem of Komjáth and Weiss

Joint work with Rodrigo Rey Carvalho.

Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space $X$ of character less than $\mathfrak b$, if $X\rightarrow(\text{top }{\omega+1})^1_\omega$, then $X\rightarrow(\text{top }{\alpha})^1_\omega$ for all $\alpha<\omega_1$.
In addition, assuming $\diamondsuit$, they constructed a space $X$ of size continuum, of character $\mathfrak b$, satisfying $X\rightarrow(\text{top }{\omega+1})^1_\omega$, but not $X\rightarrow(\text{top }{\omega^2+1})^1_\omega$.
Here, a counterexample space with the same characteristics is obtained outright in ZFC.

Downloads: