English

Countably compact groups and sequential order

General Topology 2019-03-20 v1

Abstract

We use \diamondsuit to construct, for every αω1\alpha\leq\omega_1 a sequential countably compact topological group of sequential order α\alpha. This establishes the independence of the existence of sequential countably compact non Fr\'echet groups from the usual axioms of ZFC and answers several questions of D.~Shakhmatov.

Keywords

Cite

@article{arxiv.1903.08041,
  title  = {Countably compact groups and sequential order},
  author = {Dmitri Shakhmatov and Alexander Shibakov},
  journal= {arXiv preprint arXiv:1903.08041},
  year   = {2019}
}