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

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2020
• Hauptverfasser: Bardyla, S., Gutik, O.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/188551
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: On the lattice of weak topologies on the bicyclic monoid with adjoined zero / S. Bardyla, O. Gutik // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 26–43. — Бібліогр.: 30 назв. — англ.

A Hausdorff topology τ on the bicyclic monoid with adjoined zero C⁰ is called weak if it is contained in the coarsest inverse semigroup topology on C⁰. We show that the lattice W of all weak shift-continuous topologies on C⁰ is isomorphic to the lattice SIF¹×SIF¹ where SIF¹ is the set of all shift-...