Compactification of groups and rings and nonstandard analysis

Abstract

Let G be a separated (Hausdorff) topological group and let *G be an enlargement of G (see [8]). Thus, *G (i) possesses the same formal properties as G in the sense explained in [8], and (ii) every set of subsets {Aν} of G with the finite intersection property—i.e. such that every nonempty finite subset of {Aν} has a nonempty intersection—satisfies ∩*Aν ≠ ø, where the *Aν are the extensions of the Aν in *G, respectively.