On topologization of the extended bicyclic semigroup

Oleg Gutik; Marharyta Zolotar; Oleksandra Lysetska

On topologization of the extended bicyclic semigroup

Group Theory 2026-01-22 v1 General Topology

Authors: Oleg Gutik , Marharyta Zolotar , Oleksandra Lysetska

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.

Keywords

semigroup topological semigroup bicyclic semigroup $T_1$ topology discrete topology

Cite

@article{arxiv.2601.14502,
  title  = {On topologization of the extended bicyclic semigroup},
  author = {Oleg Gutik and Marharyta Zolotar and Oleksandra Lysetska},
  journal= {arXiv preprint arXiv:2601.14502},
  year   = {2026}
}

Comments

11 pages, in Ukrainian

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