On topologization of subsemigroups of the bicyclic monoid
Abstract
We show that if a subsemigroup $S$ of the bicyclic monoid ${\mathscr{C}}(p,q)$ contains infinitely many idempotents then $S$ admits only the discrete Hausdorff shift-continuous topology. Also we proof that every right-continuous (left-continuous\emph) Hausdorff Baire topology on the semigroup $\mathscr{C}_+(a,b)$ $(\mathscr{C}_-(a,b))$ is discrete and the same statement holds for the bicyclic monoid.
Fields of Study & Subjects
Advanced Topology and Set Theory
semigroups and automata theory
Fuzzy and Soft Set Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 January 2026
- Document type
- Preprint