On general cohomology theory

Abstract

Introduction. Due to the somewhat complicated character of the original definition of the Cech cohomology groups (in terms of open coverings and direct limit groups), several alternative approaches have been proposed in the literature for the purpose of achieving better conceptual insight or greater technical convenience, or preferably both. The purpose of this note is to propose still another approach to general cohomology theory. For the sake of economy in presentation, we first state our definition of the cohomology groups HPi(X, A), for a pair of topological spaces such that A CX, and defer comments on motivation and relationship to other approaches to the concluding sections.