Intrinsic characterization of Alexander-Spanier cohomology groups of compactifications
There is an ongoing interest in extensions and elaborations of the classical Alexander-Spanier cohomology theory, abbreviated here A-S. This paper provides several references with suitable historical annotations. The main impetus of this paper is to find an intrinsic characterization of the classical A-S cohomology groups of compactifications of completely regular spaces. Towards this end, an extension of A-S cohomology theory is given on the category of pairs of uniform spaces: This construction is functorial with values in the category of abelian groups satisfying the Eilenberg-Steenrod axioms. Moreover, this theory is precompact shape invariant and as desired it captures A-S cohomology groups of compactifications of completely regular spaces. Many related classical references and historical details are also provided.
scientific article; zbMATH DE number 5597512