Equivariant uniform Alexander-Spanier cohomology theory

Abstract

In this paper we construct an equivariant cohomology functor with a contravariant coefficient system from the category of pair of uniform G spaces and G maps to the category of abelian groups, where G is a finite group. We call this Equivariant Uniform Alexander-Spanier Cohomology functor as our construction generalizes the construction of Uniform Alexander-Spanier Cohomology functor [1] on uniform spaces. We show that on the category of pair of precompact uniform G spaces, this cohomology functor satisfies all the Eilenberg-Steenrod axioms for an equivariant cohomology theory including the dimension axiom.