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.