On the special semigroup “at infinity”

This paper presents an important new technique for studying a particular compact semigroup, N∪{∞}N∪{∞}, the one-point compactification of positive integers with usual addition, which is an important semigroup. Indeed, the semigroup N∪{∞}N∪{∞} is constructed as the quotient semigroup of a particular compact right topological semigroup. In the study of such a semigroup, a major role is played by the substructures called standard oids. For instance, some of the already known results on the structure of N∪{∞}N∪{∞} are obtained as immediate consequences.