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

TL;DR

The paper proves that in pseudocompact quasitopological Korovin groups, all countable subsets are closed, discrete, and $C^*$-embedded, leading to implications about their topological properties and non-homeomorphism to certain spaces.

Contribution

It establishes new topological properties of countable subsets in pseudocompact Korovin groups and explores their non-homeomorphism to topological groups and Mal'tsev spaces.

Findings

Countable subsets are closed, discrete, and $C^*$-embedded.

Infinite pseudocompact Korovin orbits are not homeomorphic to topological groups.

Infinite pseudocompact Korovin orbits are not homeomorphic to Mal'tsev spaces.

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.