O. Gutik

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math.GR2026

On topologization of the extended bicyclic semigroup

Oleg Gutik, Marharyta Zolotar, Oleksandra Lysetska

Non-discrete semigroup $T_{1}$ -topologies on the extended bicyclic semigroup $C_{Z}$ are constructed. Also, we present topological conditions, when a semigroup (shif…

math.GR2026

On topologization of subsemigroups of the bicyclic monoid

Adriana Chornenka, Oleg Gutik

We show that if a subsemigroup $S$ of the bicyclic monoid $C (p, q)$ contains infinitely many idempotents then $S$ admits only the discrete Hausdorff shift-continuous top…

math.GR2024

On topologization of the bicyclic monoid

Adriana Chornenka, Oleg Gutik

We construct two non-discrete inverse semigroup $T_{1}$ -topologies and a compact inverse shift-continuous $T_{1}$ -topology on the bicyclic monoid $C (p, q)$ . Also we give con…

math.GR2024

On some generalization of the bicyclic semigroup: the topological version

Matija Cencelj, Oleg Gutik, Dušan Repovš

We show that every Hausdorff Baire topology $τ$ on $C = ⟨ a, b ∣ a^{2} b = a, a b^{2} = b ⟩$ such that $(C, τ)$ is a semitopological semigroup is discrete and we…