The families of right (left) translation finite subsets of a discrete infinite group Γ are defined and shown to be ideals. Their kernels ZR and ZL are identified as the closure of the set of products pq (p · q) in the Čech-Stone compactification βΓ. Consequently it is shown that the map π : βΓ → Γ , the canonical semigroup homomorphism from βΓ onto Γ , the universal semitopological semigroup co...

The universal abelian, band, and semilattice compactifications of a semitopological semigroup are characterized in terms of three function algebras. Some relationships among these function algebras and some well-known ones, from the universal compactification point of view, are also discussed.

The notion of "Semigroup compactification" which is in a sense, a generalization of the classical Bohr (almost periodic) compactlflcation of the usual additive reals R, has been studied by J.F. Berglund et. al. [2]. Their approach to the theory of semigroup compactification is based on the Gelfand-Naimark theory of commutative Calgebras, where the spectra of admissible C*-aigebras, are the semi...

Abstract We introduce the notion of an introverted Boolean algebra $\mathcal{B}$ closed-and-open subsets a topological group G, show that associated Stone space $(\nu_{\mathcal{B}} \nu_{\mathcal{B}})$ is totally disconnected semigroup compactification G and every takes this form. identify study universal compactification, semitopological G. Our main results are obtained independently Gelfand th...

we characterize function spaces of rees matrixsemigroups. then we study these spaces by using the topologicaltensor product technique.

We prove that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its the Stone-Čech compactification βS provided S is a pseudocompact openly factorizable space, which means that each map f : S → Y to a second countable space Y can be written as the composition f = g ◦ p of an open map p : X → Z onto a second countable space Z and a map g : Z → Y ...