On topologization of subsemigroups of the bicyclic monoid
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917184719028224 |
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| author | Chornenka, Adriana Gutik, Oleg |
| author_facet | Chornenka, Adriana Gutik, Oleg |
| contents | We show that if a subsemigroup $S$ of the bicyclic monoid ${\mathscr{C}}(p,q)$ contains infinitely many idempotents then $S$ admits only the discrete Hausdorff shift-continuous topology. Also we proof that every right-continuous (left-continuous\emph) Hausdorff Baire topology on the semigroup $\mathscr{C}_+(a,b)$ $(\mathscr{C}_-(a,b))$ is discrete and the same statement holds for the bicyclic monoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02100 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On topologization of subsemigroups of the bicyclic monoid Chornenka, Adriana Gutik, Oleg Group Theory General Topology 22A15, 54A10, 54E52 We show that if a subsemigroup $S$ of the bicyclic monoid ${\mathscr{C}}(p,q)$ contains infinitely many idempotents then $S$ admits only the discrete Hausdorff shift-continuous topology. Also we proof that every right-continuous (left-continuous\emph) Hausdorff Baire topology on the semigroup $\mathscr{C}_+(a,b)$ $(\mathscr{C}_-(a,b))$ is discrete and the same statement holds for the bicyclic monoid. |
| title | On topologization of subsemigroups of the bicyclic monoid |
| topic | Group Theory General Topology 22A15, 54A10, 54E52 |
| url | https://arxiv.org/abs/2601.02100 |