2021/10/30 by Hector Barrig-Acosta, Barrig-Acosta, Hector, Alan Dow +1
Mathematics · #03E04 #03E10 #03E17 #03E35 #03E65 #06E15 #54A20 #54A35 #54B10 #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2111.03783
openalex publication_date 2021/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove that in forcing extensions by a poset with finally property K over a model of GCH+\square, every compact sequentially compact space is weakly pseudoradial. We also prove the following assuming \mathfraks≤ ℵ2: (i) if X is compact weakly pseudoradial, then X is pseudoradial if and only if X cannot be mapped onto [0,1]^\mathfraks; (ii) if X and Y are compact pseudoradial spaces such that X× Y is weakly pseudoradial, then X× 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.