On the lattice of weak topologies on the bicyclic monoid with adjoined zero

• Date: 2020
• Main Authors: Bardyla, S., Gutik, O.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: lattice of topologies; bicyclic monoid; shift-continuous topology; 22A15; 06B23
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1459
• Journal Title: Algebra and Discrete Mathematics

A Hausdorff topology \(\tau\) on the bicyclic monoid with adjoined zero \(\mathcal{C}^0\) is called weak if it is contained in the coarsest inverse semigroup topology on \(\mathcal{C}^0\). We show that the lattice \(\mathcal{W}\) of all weak shift-continuous topologies on \(\mathcal{C}^0\) is isomor...