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arXiv · 1904.04416

Pseudoradial spaces and copies of $ω_1+1$

Angelo Bella·Alan Dow·Rodrigo Hernández-Gutiérrez
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Abstract

In this paper we compare the concepts of pseudoradial spaces and the recently defined strongly pseudoradial spaces in the realm of compact spaces. We show that $\mathrm{MA}+\mathfrak{c}=ω_2$ implies that there is a compact pseudoradial space that is not strongly pseudoradial. We essentially construct a compact, sequentially compact space $X$ and a continuous function $f:X\toω_1+1$ in such a way that there is no copy of $ω_1+1$ in $X$ that maps cofinally under $f$. We also give some conditions that imply the existence of copies of $ω_1$ in spaces. In particular, $\mathrm{PFA}$ implies that compact almost radial spaces of radial character $ω_1$ contain many copies of $ω_1$.

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Angelo Bella, Alan Dow, Rodrigo Hernández-Gutiérrez. 2019-04-09. Pseudoradial spaces and copies of $ω_1+1$. https://doi.org/10.1016/j.topol.2020.107070

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