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arXiv · 2601.14502

On topologization of the extended bicyclic semigroup

Oleg Gutik·Marharyta Zolotar·Oleksandra Lysetska
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Abstract

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.

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Oleg Gutik, Marharyta Zolotar, Oleksandra Lysetska. 2026-01-20. On topologization of the extended bicyclic semigroup. https://arxiv.org/abs/2601.14502

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