Stone-ČECH compactification of discrete semigroups

In this thesis some well known properties of topological semigroups andalgebraic structure of topological semigroups are presented.Then construction of the Stone-Čech compactification of β D of a discretespace D is defined and some topological properties of β D are given. Some resultson algebraic structure of β S are obtained, where S denoted a semigroup. We showthat there are 2c discrete copies of Z in each of the maximal groups in the smallestideal, and that any two of these meet only in the identity.Finally cancellativity of β S is studied and some conditions is obtained oncancellativity of β S .Key Words: Discrete semigroup, homomorphism, isomorphism, homoemorphism,cancellativity, finite group