On the weak pseudoradiality of CSC spaces

Abstract

In this paper we prove that in forcing extensions by a poset with finally property K over a model of GCH+ , every compact sequentially compact space is weakly pseudoradial. This improves Theorem 4 in [?dow1996more]. We also prove the following assuming s ≤ א2: (i) if X is compact weakly pseudoradial, then X is pseudoradial if and only if X cannot be mapped onto [0, 1]s; (ii) if X and Y are compact pseudoradial spaces such that X × Y is weakly pseudoradial, then X × Y is pseudoradial. This 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.