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arXiv · 2401.06594

On some generalization of the bicyclic semigroup: the topological version

Matija Cencelj·Oleg Gutik·Dušan Repovš
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Abstract

We show that every Hausdorff Baire topology $\tau$ on $\mathcal{C}=\langle a,b\mid a^2b=a, ab^2=b\rangle$ such that $(\mathcal{C},\tau)$ is a semitopological semigroup is discrete and we construct a nondiscrete Hausdorff semigroup topology on $\mathcal{C}$. We also discuss the closure of a semigroup $\mathcal{C}$ in a semitopological semigroup and prove that $\mathcal{C}$ does not embed into a topological semigroup with the countably compact square.

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Matija Cencelj, Oleg Gutik, Dušan Repovš. 2024-01-12. On some generalization of the bicyclic semigroup: the topological version. https://doi.org/10.30970/vmm.2022.94.056-071

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