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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 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...

Topos based homology theory

M. V. Mielke (1993)

Commentationes Mathematicae Universitatis Carolinae

In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the interval based homotopies and, for toposes, the excisions represented by “cutting out” subobjects. The...

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 theories...

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