The Stone-Čech compactification of discrete semigroups is a tool of central importance in several areas of mathematics, and has been studied extensively. We think of the Stone-Čech compactification of a discrete abelian semigroup G as the set βG of ultrafilters on G, where the point x ∈ G is identified with the principal ultrafilter {A ⊆ G ∣∣x ∈ A}, and the basic open sets are those of the form...

Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these continuous mappings — also tools from Model Theory. We illustrate by showing that 1) thě Cech-Stone remainder [0, ∞) has a universality property akin to tha...

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...