Cohomology theories on spaces
Author:
E. Spanier
Journal:
Trans. Amer. Math. Soc. 301 (1987), 149-161
MSC:
Primary 55N40; Secondary 55N35
DOI:
https://doi.org/10.1090/S0002-9947-1987-0879567-3
MathSciNet review:
879567
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Abstract: In this paper a previously proven uniqueness theorem for nonnegative cohomology theories on the same space is extended to cohomology theories on the same finite-dimensional space. In this form it is applicable to extraordinary cohomology theories. An example is given to show that the theorem does not hold without finite dimensionality.
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, New Jersey, 1952. MR 0050886
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- Max Karoubi, $K$-theory, Springer-Verlag, Berlin-New York, 1978. An introduction; Grundlehren der Mathematischen Wissenschaften, Band 226. MR 0488029
- Jimmie D. Lawson, Comparison of taut cohomologies, Aequationes Math. 9 (1973), 201–209. MR 331372, DOI https://doi.org/10.1007/BF01832627
- William S. Massey, Homology and cohomology theory, Marcel Dekker, Inc., New York-Basel, 1978. An approach based on Alexander-Spanier cochains; Monographs and Textbooks in Pure and Applied Mathematics, Vol. 46. MR 0488016
- Ernest Michael, Local properties of topological spaces, Duke Math. J. 21 (1954), 163–171. MR 62424
- Edwin H. Spanier, Algebraic topology, Springer-Verlag, New York-Berlin, 1981. Corrected reprint. MR 666554
- E. Spanier, Cohomology isomorphisms, Symposium on Algebraic Topology in honor of José Adem (Oaxtepec, 1981), Contemp. Math., vol. 12, Amer. Math. Soc., Providence, R.I., 1982, pp. 315–329. MR 676339
- Joseph L. Taylor, A counterexample in shape theory, Bull. Amer. Math. Soc. 81 (1975), 629–632. MR 375328, DOI https://doi.org/10.1090/S0002-9904-1975-13768-2
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© Copyright 1987
American Mathematical Society