Intrinsic characterization of Alexander-Spanier cohomology groups of compactifications

In this paper we construct a uniform Alexander-Spanier cohomology functor from the category of pairs of uniform spaces to the category of abelian groups. We show that this functor satisfies all Eilenberg-Steenrod axioms on the category of pairs of precompact uniform spaces, is precompact uniform shape invariant and intrinsically, in terms of uniform structures, describes the Alexander-Spanier cohomology groups of compactifications of completely regular spaces.