Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777795 | Topology and its Applications | 2017 | 16 Pages |
Abstract
A space X is selectively sequentially pseudocompact if for every family {Un:nâN} of non-empty open subsets of X, one can choose a point xnâUn for every nâN in such a way that the sequence {xn:nâN} has a convergent subsequence. Let G be a group from one of the following three classes: (i) V-free groups, where V is an arbitrary variety of Abelian groups; (ii) torsion Abelian groups; (iii) torsion-free Abelian groups. Under the Singular Cardinal Hypothesis SCH, we prove that if G admits a pseudocompact group topology, then it can also be equipped with a selectively sequentially pseudocompact group topology. Since selectively sequentially pseudocompact spaces are strongly pseudocompact in the sense of GarcÃa-Ferreira and Ortiz-Castillo, this provides a strong positive (albeit partial) answer to a question of GarcÃa-Ferreira and Tomita.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Alejandro Dorantes-Aldama, Dmitri Shakhmatov,