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

Abstract

We show that all countable subsets of any pseudocompact quasitopological group in the form of a Korovin orbit are closed, discrete, and $C^{\ast }$-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.