Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 597-614
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S. V. Petkova. On the axioms of homology theory. Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 597-614. http://geodesic.mathdoc.fr/item/SM_1973_19_4_a5/
@article{SM_1973_19_4_a5,
author = {S. V. Petkova},
title = {On~the axioms of homology theory},
journal = {Sbornik. Mathematics},
pages = {597--614},
year = {1973},
volume = {19},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1973_19_4_a5/}
}
TY - JOUR
AU - S. V. Petkova
TI - On the axioms of homology theory
JO - Sbornik. Mathematics
PY - 1973
SP - 597
EP - 614
VL - 19
IS - 4
UR - http://geodesic.mathdoc.fr/item/SM_1973_19_4_a5/
LA - en
ID - SM_1973_19_4_a5
ER -
%0 Journal Article
%A S. V. Petkova
%T On the axioms of homology theory
%J Sbornik. Mathematics
%D 1973
%P 597-614
%V 19
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1973_19_4_a5/
%G en
%F SM_1973_19_4_a5
We give an axiomatization for homology and cohomology theory in the categories $\mathscr A$ and $\mathscr B$ of countable locally finite polyhedra and of locally compact metrizable spaces, respectively, with proper mappings; in the category $\mathscr B_0$ of metrizable compacta and continuous mappings; and (for cohomology) in the category $\mathscr B$ of locally compact metrizable spaces and arbitrary continuous mappings. In $\mathscr B$ we determine the kernel of the natural homomorphism $\varphi\colon H^n(X)\to\varprojlim H^n(C)$ over compact $C$ for a $\Pi$-additive cohomology (in particular, for Aleksandrov–Čech cohomology). Finally, we analyze the axioms of Sklyarenko (Math. Sb. (N.S.) 85(127) (1971), 201–223). Bibliography: 6 titles.
