The continuity axiom and the Čech homology

  • Tadashi Watanabe
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1283)

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References

  1. [1]
    P. Bacon, Axioms for the Cech cohomology of paracompacta, Pacific J. Math. 52(1974) 7–9.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    —, Continuous functors, General Topology Appl. 5(1975) 321–331.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    G.E. Bredon, Sheaf theory, MaGraw-Hill Book Company, 1967.Google Scholar
  4. [4]
    C.E. Capel, Inverse limit spaces, Duke Math. J. 21(1954) 233–245.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    S. Deo, On the tautness property of Alexander-Spanier cohomology, Proc. Amer. Math. Soc. 52(1975) 441–444.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton, New Jersey, Princeton Univ. Press, 1952.CrossRefMATHGoogle Scholar
  7. [7]
    R. Godement, Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1958.MATHGoogle Scholar
  8. [8]
    S.T. Hu, Theory of retracts, Wayne State Univ. Press, Detroit, 1965.MATHGoogle Scholar
  9. [9]
    J.D. Lawson, Comparison of taut cohomologies, Aequationes Math. 9(1973) 201–209.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    C.N. Lee and F. Raymond, Čech extensions for contravariant functors, Trans. Math. Soc. 133(1968) 415–434.MathSciNetMATHGoogle Scholar
  11. [11]
    S. Mardešić, Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114(1981) 53–78.MathSciNetMATHGoogle Scholar
  12. [12]
    —, On resolutions for pairs of spaces, Tsukuba J. Math. 8(1984) 81–93.MathSciNetMATHGoogle Scholar
  13. [13]
    —, On the homotopy type of ANRs for p-paracompacta, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 27(1979) 803–808.MathSciNetMATHGoogle Scholar
  14. [14]
    — and J. Segal, Shape theory, the inverse system approach, North-Holland Publishing Company, Amsterdam, 1982.MATHGoogle Scholar
  15. [15]
    E. Michael, A note on paracompact spaces, Proc. Amer. Math. Soc. 4(1953) 831–838.MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    J. Milnor, On axiomatic homology theory, Pacific J. Math. 12(1962) 337–341.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    —, On the Steenrod homology theory, Univ. of California, Berkeley, CA 1960 (mimeographed).MATHGoogle Scholar
  18. [18]
    K. Morita, On shapes of topological spaces, Fund. Math. 86(1975) 251–259.MathSciNetMATHGoogle Scholar
  19. [19]
    —, Čech cohomology and covering dimension for topological spaces, Fund. Math. 87(1975) 31–52.MathSciNetMATHGoogle Scholar
  20. [20]
    K. Nagami, Dimension theory, Academic Press, New York, 1970.MATHGoogle Scholar
  21. [21]
    S.V. Petkova, On the axioms of homology theory, Math. Sbornik, 90(1973) 607–624 = Math. USSR Sbornik 19(1973) 597–614.MathSciNetGoogle Scholar
  22. [22]
    E.G. Skljarenko, Homology theory and the exactness axiom, Uspekhi Math. Nauk 245(1969) 87–140 = Russian Math. Surveys 24(1969) 91–142.MathSciNetGoogle Scholar
  23. [23]
    —, Uniqueness theorems in homology theory, Math. Sbornik, 85(1971) 201–223 = Math. USSR Sbornik, 14(1971) 199–218.MathSciNetGoogle Scholar
  24. [24]
    E.H. Spanier, Algebraic topology, MaGraw-Hill Book Company, Inc., New York, 1966.MATHGoogle Scholar
  25. [25]
    —, Tautness for Alexander-Spanier cohomology, Pacific J. Math. 75(1978) 561–563.MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    N.E. Steenrod, Regular cycles of compact metric spaces, Ann. of Math. (2) 41(1940) 833–851.MathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    K.A. Stinikov, Combinatorial topology of nonclosed sets I. The first duality law; spectral duality, Math. Sb. N. S. 34(1954) 3–54 = Amer. Math. Soc. Transl. (2)15(1960) 245–295.MathSciNetGoogle Scholar
  28. [28]
    A.D. Wallace, The map excision theorem, Duke Math. J. 19(1952) 177–182.MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    T. Watanabe, Approximative expansions of maps into inverse systems, to appear in Proc. of Banach Math. Center.Google Scholar
  30. [30]
    —, Čech homology, Steenrod homology and strong homology I, to appear in Glasnik Mat.Google Scholar
  31. [31]
    —, Approximative Shape I-IV, to appear in Tsukuba J. Math.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Tadashi Watanabe
    • 1
  1. 1.Department of Mathematics, Faculty of EducationUniversity of YamaguchiYamaguchi CityJapan

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