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 on X both of which are additive or both of which are weakly additive which recomposes the previously known comparison theorems.
@article{urn:eudml:doc:41120,
title = {Weakly additive cohomology.},
journal = {Publicacions Matem\`atiques},
volume = {34},
year = {1990},
pages = {145-150},
zbl = {0707.55005},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41120}
}
Spanier, Edwin. Weakly additive cohomology.. Publicacions Matemàtiques, Tome 34 (1990) pp. 145-150. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41120/