On topologization of the extended bicyclic semigroup
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914268667969536 |
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| author | Gutik, Oleg Zolotar, Marharyta Lysetska, Oleksandra |
| author_facet | Gutik, Oleg Zolotar, Marharyta Lysetska, Oleksandra |
| contents | Non-discrete semigroup $T_1$-topologies on the extended bicyclic semigroup $\mathscr{C}_\mathbb{Z}$ are constructed. Also, we present topological conditions, when a semigroup (shift-continuous) $T_1$-topology on $\mathscr{C}_\mathbb{Z}$ is discrete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14502 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On topologization of the extended bicyclic semigroup Gutik, Oleg Zolotar, Marharyta Lysetska, Oleksandra Group Theory General Topology 22A15, 54C08, 54D10, 54H10 Non-discrete semigroup $T_1$-topologies on the extended bicyclic semigroup $\mathscr{C}_\mathbb{Z}$ are constructed. Also, we present topological conditions, when a semigroup (shift-continuous) $T_1$-topology on $\mathscr{C}_\mathbb{Z}$ is discrete. |
| title | On topologization of the extended bicyclic semigroup |
| topic | Group Theory General Topology 22A15, 54C08, 54D10, 54H10 |
| url | https://arxiv.org/abs/2601.14502 |