For a unital foundation topological *-semigroup S whose representations separate points of S, we show that the spectrum of the Fourier-Stieltjes algebra B(S) is a compact semitopological semigroup. We also calculate B(S) for several examples of S.

A group is finitely axiomatizable (FA) in a class C if it can be determined up to isomorphism within by sentence the first-order language of theory. We show that profinite groups various kinds are FA groups, or pro- p for some prime p. Both algebraic and model-theoretic methods developed purpose. Reasons why certain cannot also discussed.

We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. resolve a serious deficit in existing theory by constructing good notion of presheaves, with suitable sheafification functor. Using sheafification, we develop general modules ring, give explicit constructions infinite products and introduce an analogue skyscraper sheaves. These results underlie re...