On non-topologizable semigroups.
We give conditions on a semigroup 
under which every Hausdorff left (right) topology on is discrete. Continuum many subsemigroups of the bicyclic monoids with such property will be presented.
On non-topologizable semigroups.
We give conditions on a semigroup under which every Hausdorff left (right) topology on is discrete. Continuum many subsemigroups of the bicyclic monoids with such property will be presented.