Countably compact groups without nontrivial convergent sequences
Abstract
We construct, in $\mathsf{ZFC}$, a countably compact subgroup of $2^{\mathfrak{c}}$ without nontrivial convergent sequences, answering an old problem of van Douwen. As a consequence we also prove the existence of two countably compact groups $\mathbb{G}_{0}$ and $\mathbb{G}_{1}$ such that the product $\mathbb{G}_{0} \times \mathbb{G}_{1}$ is not countably compact, thus answering a classical problem of Comfort.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.12675
 Bibcode:
 2020arXiv200612675H
 Keywords:

 Mathematics  General Topology;
 Mathematics  Logic;
 22A05;
 03C20 (Primary) 03E05;
 54H11 (Secondary)
 EPrint:
 21 pages, to be published in Transactions of the American Mathematical Society