A Stone-type theorem for Abelian semigroups (Q1106340)

The main result of the paper reads as follows: Let A and B be disjoint subsemigroups of the Abelian semigroup S. Then there exist complementary subsemigroups \(A^*\) and \(B^*\) in S such that \(A\subseteq A^*\) and \(B\subseteq B^*\). (Two sets in S are called complementary if they form a partition of S.) Applying the above result, Stone's separation theorem for disjoint convex sets can easily be deduced.