English

All countable subsets of pseudocompact quasitopological Korovin groups are closed, discrete and $C^\ast$-embedded

General Topology 2023-08-22 v3

Abstract

We show that all countable subsets of any pseudocompact quasitopological group in the form of a Korovin orbit are closed, discrete, and CC^\ast-embedded. Consequently, any infinite pseudocompact Korovin orbit is not homeomorphic to a topological group. Moreover, infinite pseudocompact Korovin orbits are not homeomorphic to any Mal'tsev space.

Keywords

Cite

@article{arxiv.2302.11251,
  title  = {All countable subsets of pseudocompact quasitopological Korovin groups are closed, discrete and $C^\ast$-embedded},
  author = {Evgenii Reznichenko and Mikhail Tkachenko},
  journal= {arXiv preprint arXiv:2302.11251},
  year   = {2023}
}