On topologization of the bicyclic monoid
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909228540624896 |
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| author | Chornenka, Adriana Gutik, Oleg |
| author_facet | Chornenka, Adriana Gutik, Oleg |
| contents | We construct two non-discrete inverse semigroup $T_1$-topologies and a compact inverse shift-continuous $T_1$-topology on the bicyclic monoid ${\mathscr{C}}(p,q)$. Also we give conditions on a $T_1$-topology $τ$ on ${\mathscr{C}}(p,q)$ to be discrete. In particular, we show that if $τ$ is an inverse semigroup $T_1$-topology on ${\mathscr{C}}(p,q)$ which satisfies one of the following conditions: $τ$ is Baire, $τ$ is quasi-regular or $τ$ is semiregular, then $τ$ is discrete. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_05836 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On topologization of the bicyclic monoid Chornenka, Adriana Gutik, Oleg Group Theory General Topology 22A15, 54A10, 54D10, 54D30, 54D45 We construct two non-discrete inverse semigroup $T_1$-topologies and a compact inverse shift-continuous $T_1$-topology on the bicyclic monoid ${\mathscr{C}}(p,q)$. Also we give conditions on a $T_1$-topology $τ$ on ${\mathscr{C}}(p,q)$ to be discrete. In particular, we show that if $τ$ is an inverse semigroup $T_1$-topology on ${\mathscr{C}}(p,q)$ which satisfies one of the following conditions: $τ$ is Baire, $τ$ is quasi-regular or $τ$ is semiregular, then $τ$ is discrete. |
| title | On topologization of the bicyclic monoid |
| topic | Group Theory General Topology 22A15, 54A10, 54D10, 54D30, 54D45 |
| url | https://arxiv.org/abs/2403.05836 |