Ideals of the Stone-Čech compactification of semigroups (Q1065163)

The author answers the question as to whether it is always true that the closure of the minimal ideal of a compact left-topological semigroup T is contained in \(T^ 2\). (This is certainly true if T is separately continuous.) He defines a large class of semigroups, including the Stone- Čech compactifications of \(({\mathbb{N}},+)\) and (\({\mathbb{N}},\cdot)\), for which the result is shown to be false.