Resumen de Residual bounds for compact totally disconnected algebras

Marcel Jackson

• A Boolean topological algebra is a general algebra with a compatible topology that is compact and totally disconnected. It is well known that every Boolean topological semigroup, group or ring is topologically residually finite; that is, every pair of distinct elements can be separated by a continuous homomorphism into a (discretely topologised) finite algebra. We examine the possible residual bounds for Boolean topological algebras in relation to their non-topological residual bound, with particular emphasis given to groups and completely simple semigroups. Amongst the results is the undecidability of the problem of determining if all Boolean topological models of a finite set of identities are profinite