On the weak pseudoradiality of CSC spaces
Volume 258 / 2022
Fundamenta Mathematicae 258 (2022), 249-264
MSC: Primary 03E04; Secondary 03E10, 03E17, 03E35, 03E65, 06E15, 54A20, 54A35, 54B10.
DOI: 10.4064/fm135-1-2022
Published online: 10 June 2022
Abstract
We prove that in forcing extensions by a poset with finally property K over a model of ${\rm GCH}+\square $, every compact sequentially compact space is weakly pseudoradial. This improves Theorem 4 in [A. Dow et al., Topology Appl. 72 (1996)]. We also prove the following assuming $\mathfrak {s}\leq \aleph _2$: (i) if $X$ is compact weakly pseudoradial, then $X$ is pseudoradial if and only if $X$ cannot be mapped onto $[0,1]^\mathfrak {s}$; (ii) if $X$ and $Y$ are compact pseudoradial spaces such that $X\times Y$ is weakly pseudoradial, then $X\times Y$ is pseudoradial. These results add to the wide variety of partial answers to the question by Gerlits and Nagy of whether the product of two compact pseudoradial spaces is pseudoradial.
