Let G be a profinite group with a countable basis of neighborhoods of the identity. A cohomology and homology theory for the group G with non-discrete topological coefficients is developed, improving previous expositions of the subject (see [Wi], [R–Z] and [S-W]). Though the category of topological G-modules considered is additive but not abelian, there is a theory of derived functors. All stan...

Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion of any abstract algebra is the extended Stone dual space of the Boolean algebra of recognisable subsets of the abstract algebra endowed with certain residuat...

We present an extension of a statically typed language with a special type Dynamic and explicit type tagging and checking operations (coercions). Programs in run-time typed languages are viewed as incomplete programs that are to be completed to well-typed programs by explicitly inserting coercions into them. Such completions are generally not unique. If the meaning of an incomplete program is t...

A directed set I is a partially ordered set such that for all i, j ∈ I there exists a k ∈ I such that k ≥ i and k ≥ j. An inverse system of groups is a collection of groups {Gi} indexed by a directed set I together with group homomorphisms πij : Gi −→ Gj whenever i ≥ j such that πii = idGi and πjk ◦ πij = πik. Let H be a group. We call a family of homomorphisms {ψi : H −→ Gi : i ∈ I} compatible...