On some generalization of the bicyclic semigroup: the topological version
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909071250030592 |
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| author | Cencelj, Matija Gutik, Oleg Repovš, Dušan |
| author_facet | Cencelj, Matija Gutik, Oleg Repovš, Dušan |
| contents | We show that every Hausdorff Baire topology $τ$ on $\mathcal{C}=\langle a,b\mid a^2b=a, ab^2=b\rangle$ such that $(\mathcal{C},τ)$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_06594 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some generalization of the bicyclic semigroup: the topological version Cencelj, Matija Gutik, Oleg Repovš, Dušan Group Theory General Topology Primary 22A15, 20M20, Secondary 20M05, 54C25, 54E52 We show that every Hausdorff Baire topology $τ$ on $\mathcal{C}=\langle a,b\mid a^2b=a, ab^2=b\rangle$ such that $(\mathcal{C},τ)$ 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. |
| title | On some generalization of the bicyclic semigroup: the topological version |
| topic | Group Theory General Topology Primary 22A15, 20M20, Secondary 20M05, 54C25, 54E52 |
| url | https://arxiv.org/abs/2401.06594 |