On some generalization of the bicyclic semigroup: the topological version

Matija Cencelj, Oleg Gutik, Dusan Repovs


We show that every Hausdorff Baire topology τ on C=⟨ a,b| a2b=a, ab2=b⟩ such that (C,τ) is a semitopological semigroup is discrete and we construct a nondiscrete Hausdorff semigroup topology on C. We also discuss the closure of a semigroup C in a semitopological semigroup and prove that C does not embed into a topological semigroup with the countably compact square.

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DOI: http://dx.doi.org/10.30970/vmm.2022.94.056-071


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