On some generalization of the bicyclic semigroup: the topological version

Matija Cencelj, Oleg Gutik, Dušan Repovš

We show that every Hausdorff Baire topology $\tau$ on $\mathcal{C}=⟨a,b\mid a^{2}b=a,a{b}^2=b⟩$ such that $(\mathcal{C},\tau )$ is a semitopological semigroup is discrete and we…