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Cohomology theories on compact and locally compact spaces.

Edwin Spanier — 1986

Revista Matemática Iberoamericana

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 C, the category of all compact Haudorff spaces and continuous functions between them, and C, 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...

Weakly additive cohomology.

Edwin Spanier — 1990

Publicacions Matemàtiques

In this paper the concept of weakly additive cohomology theory is introduced as a variant of the known concept of additive cohomology theory. It is shown that for a closed A in X the singular homology of the pair (X, X-A) (with some fixed cohomology group) regarded as a furcter of A is a weakly additive cohomology theory on any collectionwise normal space X. Furthermore, every compactly supported cohomology theory is weakly additive. The main result is a comparison theorem for two cohomology...

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