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

Evgenii Reznichenko; Mikhail Tkachenko

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arXiv · 2302.11251

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

Evgenii Reznichenko·Mikhail Tkachenko

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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.

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Evgenii Reznichenko, Mikhail Tkachenko. 2023-02-22. All countable subsets of pseudocompact quasitopological Korovin groups are closed, discrete and $C^\ast$-embedded. https://arxiv.org/abs/2302.11251

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