On some generalization of the bicyclic semigroup: the topological version

Cencelj, Matija (author), Gutik, Oleg (author), Repovš, Dušan (author)

We show that every Hausdorff Baire topology $\tau$ on ${\cal C} = \langle a,b | a^2b=a, ab^2=b \rangle$ such that $({\cal C},\tau)$ is a semitopological semigroup is discrete and we construct a nondiscrete Hausdorff semigroup topology on ${\cal C}$. We also discuss the closure of a semigroup ${\cal C}$ in a semitopological semigroup and prove that ${\cal C}$ does not embed into a topological semigroup with the countably compact square.

• Language: English
• Keywords: topological semigroup, semitopological semigroup, bicyclic semigroup, closure, embedding, Baire space
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2022
• Number of pages: Str. 56-71
• Numbering: Iss. 94
• PID: 20.500.12556/RUL-154164
• UDC: 512.536
• ISSN on article: 2078-3744
• DOI: 10.30970/vmm.2022.94.056-071
• COBISS.SI-ID: 182170115

Copyright

Recenzirani rokopis članka je v Repozitorij Univerze v Ljubljani shranjen z dovoljenjem založnika. (Datum opombe: 29. 1. 2024)

• Publication date in RUL: 29.01.2024

CENCELJ, Matija, GUTIK, Oleg and REPOVŠ, Dušan, 2022, On some generalization of the bicyclic semigroup: the topological version. Vìsnik Lʹvìvsʹkogo unìversitetu. Serìâ mehaniko-matematična = Visnyk of the Lviv University. Series mechanics and mathematics [online]. 2022. Vol. 94, p. 56–71. [Accessed 11 April 2025]. DOI 10.30970/vmm.2022.94.056-071. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=154164

Record is a part of a journal

• Title: Vìsnik Lʹvìvsʹkogo unìversitetu. Serìâ mehaniko-matematična = Visnyk of the Lviv University. Series mechanics and mathematics
• Shortened title: Vìsn. Lʹvìv. unìv., Ser. meh.-mat.
• Publisher: Lʹvìvsʹkij nacìonalnij unìversitet ìmenì Ìvana Franka
• ISSN: 2078-3744
• COBISS.SI-ID: 15881305

Secondary language

• Language: Ukrainian
• Keywords: топологічна напівгрупа, напівтопологічна напівгрупа, біциклічна напівгрупа, замикання, занурення, берівський простір