Resumen de Cohomology Theories on Compact and Locally Compact Spaces.

E. Spanier

• This paper is devoted to an exposition of cohomology theories on categories of spaces where the cohomology theories satisfy the type of axiom system considered in [1, 12, 16, 17, 18]. The categories considered are Ccomp, the category of all compact Haudorff spaces and continuous functions between them, and Cloc comp, the category of all locally compact Hausdorff spaces and proper continuous functions between them. The fundamental uniqueness theorem for cohomology theories on a finite dimensional space implies a corresponding uniqueness theorem for cohomology theories on either of these two categories. The proof involves an extension of the uniqueness theorem for finite dimensional spaces to compact spaces which contrasts with the usual type of proof which involves a uniqueness proof for polyhedra and an extension to compact spaces.