Geodesic
On the axioms of homology theory
Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 597-614 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {S. V. Petkova},
     title = {On~the axioms of homology theory},
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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/

[1] E. G. Sklyarenko, “Teoriya gomologii i aksioma tochnosti”, Uspekhi matem. nauk, XXIV:5 (1969), 87–140

[2] E. G. Sklyarenko, “Teoremy edinstvennosti v teorii gomologii”, Matem. sb., 85 (127) (1971), 201–223 | Zbl

[3] N. Stinrod, S. Eilenberg, Osnovaniya algebraicheskoi topologii, IL, Moskva, 1958

[4] J. Milnor, “On axiomatic homology theory”, Pacific J. Math., 12:1 (1962), 337–341 | MR | Zbl

[5] A. Borel, J. C. Moore, “Homology theory for locally compact spaces”, Michigan Math. J., 7 (1960), 137–160 | DOI | MR

[6] I. James, J. H. C. Whitehead, “Homology with zero coefficients”, Quart. J. Math., 9:36 (1958), 317–320 | DOI | MR | Zbl