A semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup with an identity element is called monoid. This tag is most frequently used for questions related to the concept of semigroups in the context of abstract algebra. Please use the more specific tag (semigroup-of-operators) whenever appropriate.
Topological (and left/right topological) semigroups are also studied. Perhaps the best know result in this area is Ellis-Numakura lemma. Using Ellis-Numakura lemma, existence of idempotent ultrafilters can be shown.