Weakly additive cohomology.

Edwin Spanier

Publicacions Matemàtiques (1990)

  • Volume: 34, Issue: 1, page 145-150
  • ISSN: 0214-1493

Abstract

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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.

How to cite

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Spanier, Edwin. "Weakly additive cohomology.." Publicacions Matemàtiques 34.1 (1990): 145-150. <http://eudml.org/doc/41120>.

@article{Spanier1990,
abstract = {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.},
author = {Spanier, Edwin},
journal = {Publicacions Matemàtiques},
keywords = {Cohomología; homomorphism between cohomology theories; weakly additive; para-compact supports; n-equivalence},
language = {eng},
number = {1},
pages = {145-150},
title = {Weakly additive cohomology.},
url = {http://eudml.org/doc/41120},
volume = {34},
year = {1990},
}

TY - JOUR
AU - Spanier, Edwin
TI - Weakly additive cohomology.
JO - Publicacions Matemàtiques
PY - 1990
VL - 34
IS - 1
SP - 145
EP - 150
AB - 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.
LA - eng
KW - Cohomología; homomorphism between cohomology theories; weakly additive; para-compact supports; n-equivalence
UR - http://eudml.org/doc/41120
ER -

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