Subsemigroup
= Subsemigroup
A subsemigroup is a nonempty subset of a <semigroup> closed under its <associative operation>. In a <compact Hausdorff space> carrying a <left-topological semigroup>, descending chains of nonempty compact subsemigroups have a nonempty compact subsemigroup as their intersection. This supplies the minimal object used in the <Ellis–Numakura lemma>.