Semigroup compactification of projective limits of topological semigroups

The purpose of this paper is to present some results concerning semigroup compactifications. It is shown that the limit of the projective system of semigroup compactifications of a topological semigroup S itself is a semigroup compactification of S. Also we consider Sα, φαβα ⩽ β ϵ D to be a projective system of topological monoids with Bohr compactifications (β0α, βα)α ϵ D and show that limα is a Bohr compactification of limSα.