Literature Cited
A. Dold, “Zur Homotopietheorie der Kettenhomplexe,” Math. Ann.,140, 278–298 (1960).
J. Milnor, On the Steenrod Homology Theory, Princeton (1960) [mimeographed].
V. I. Kyz'minov and I. A. Shvedov, “Quasiexact sequences of complex and hyperhomologies,” Sibirsk. Matem. Zh.,14, No. 4, 791–805 (1973).
Kh. N. Inasaridze, “On an exact homology,” Proceedings of the Tbilis Mathematics Institute,41, 128–142 (1972).
A. Borel and J. C. Moore, “Homology theory for locally compact spaces,” Mich. Math. J.,7, 137–160 (1960).
V. I. Kuz'minov and I. A. Shvedov, “On the homologies generated by cohomology functors,” Dokl. Akad. Nauk SSSR,200, No. 4, 764–766 (1971).
A. Grothendiek, On Some Problems of the Homological Algebra [Russian translation], Inostrannoi Literatura, Moscow (1961).
G. Nöbeling, Cohomologie-Moduln über Abelschen Halbgruppen, Bonner Mathematische Schriften, Vol. 12, Bonn (1960).
R. Deheuvels, “Homologie des ensembles ordoneés et espaces topologiques,” Bull. Soc. Math. France,90, No. 2, 261–321 (1962).
L. Kaup and M. S. Keane, “Inductive Limiten endlich erzeugter freier Moduln,” Manuscr. Math.,1, No. 1, 9–21 (1969).
P. S. Aleksandrov, “A general homology theory,” Uchenye Zapiski Novosibirskogo Gosudarstvennogo Universiteta, No. 5, 3–60 (1940).
R. Godement, Algebraic Topology and Sheaf Theory [Russian translation], Inostrannoi Literatura, Moscow (1961).
N. Steenrod and S. Eilenberg, Foundations of Algebraic Topology, Princeton Univ. Press, Princeton (1952).
G. S. Chogoshvili, “On the equivalence of the functional and the spectral homology theories,” Izv. Akad. Nauk SSSR, Seriya Matem.,15, 421–438 (1951).
S. Lefschetz, Algebraic Topology, American Math. Soc., Providence (1942).
E. G. Sklyarenko, “Homology theory and the exactness axiom,” Uspekhi Matem. Nauk,24, No. 5, 87–140 (1969).
L. D. Mdzinarishvili, “On the equivalence of the Kolmogorov and the Steenrod homology theories,” Proceedings of the Tbilis Mathematics Institute,41, 143–163 (1973).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 5, pp. 1083–1102, September–October, 1974.
Rights and permissions
About this article
Cite this article
Kuz'minov, V.I., Shvedov, I.A. Spectra of coverings in the homology and the cohomology theories of topological spaces. Sib Math J 15, 763–775 (1974). https://doi.org/10.1007/BF00966436
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00966436