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