Skip to main content
Log in

Local homology and dimensional full-valuedness

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

A natural criterion for dimensional full-valuedness of locally compact spaces with finitely generated local homology is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Dyer, “On the dimension of products,” Fund. Math. 47(2), 141–160 (1959).

    MATH  Google Scholar 

  2. K. Borsuk, “Opening of the conference on geometric topology,” in Proceedings of the International Conference on Geometric Topology, Warszawa, August 24–September 2, 1978 (PWN, Warszawa, 1980), pp. 12–14

    Google Scholar 

  3. A. N. Dranishnikov, “Homological dimension theory,” Uspekhi Mat. Nauk 43(4), 11–55 (1988) [Russian Math. Surveys 43 (4), 11–63 (1988)].

    Google Scholar 

  4. A. N. Dranishnikov, “On the dimension of the product of ANR-compacta,” Dokl. Akad. Nauk SSSR 300(5), 1045–1049 (1988) [Soviet Math. Dokl. 37 (3), 769–773 (1988)].

    Google Scholar 

  5. J. E. West, “Mapping Hilbert cube manifolds to ANR’s: a solution of a conjecture of Borsuk,” Ann. of Math. (2) 106(1), 1–18 (1977).

    Article  Google Scholar 

  6. T. A. Chapman, Lectures on Hilbert Cube Manifolds (American Mathematical Society, Providence, RI, 1976; Mir, Moscow, 1981).

    MATH  Google Scholar 

  7. A. E. Kharlap [Harlap], “Local homology and cohomology, homological dimension, and generalized manifolds,” Mat. Sb. (N. S.) 96(138)(3), 347–373 (1975).

    Google Scholar 

  8. G. E. Bredon, Sheaf Theory, 2nd ed. (Graduate Texts in Mathematics, 170, Springer-Verlag, New York, 1997; Nauka, Moscow, 1988).

    MATH  Google Scholar 

  9. E. G. Sklyarenko, “On homological products,” Izv. Ross. Akad. Nauk Ser. Mat. 61(1), 157–176 (1997) [Izv. Math. 61 (1), 161–181 (1997)]

    Google Scholar 

  10. E. G. Sklyarenko, “On the homology theory associated with Aleksandrov-Čechcohomology,” Uspekhi Mat. Nauk 34(6), 90–118 (1979) [Russ. Math. Surv. 34 (6), 103–137 (1979)]

    MATH  Google Scholar 

  11. E. M. Beniaminov and E. G. Skljarenko [Sklyarenko], “Local cohomology groups,” Dokl. Akad. Nauk SSSR 176(6), 987–990 (1967) [Soviet Math. Dokl. 8, 1221–1225 (1967)]

    Google Scholar 

  12. W. J. R. Mitchell, “Homology manifolds, inverse systems and cohomological local connectedness,” J. London Math. Soc. (2) 19(2), 348–358 (1979).

    Article  MATH  Google Scholar 

  13. D. Rote, “Peripheral cohomological local connectedness,” Fund. Math. 116(1), 53–66 (1983).

    Google Scholar 

  14. E. G. Skljarenko [Sklyarenko], “On the theory of generalized manifolds,” Izv. Akad. Nauk SSSR Ser. Mat. 35(4), 831–843 (1971)

    Google Scholar 

  15. D. Rote [Rothe], “The characterization of homological dimension by local homology and cohomology,” Math. Nachr. 113, 53–57 (1983).

    Article  Google Scholar 

  16. V. I. Kuz’minov, “Homological dimension theory,” Uspekhi [Uspehi] Mat. Nauk, 23(5), 3–49 (1968) [Russ. Math. Surv. [23 (5), 1–45 (1968)]

    MATH  Google Scholar 

  17. S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology (Princeton University Press, Princeton, New Jersey, 1952; Fizmatgiz, Moscow, 1958).

    MATH  Google Scholar 

  18. K. Borsuk, Theory of Retracts. Monografie Matematyczne, Torn 44 (Panstwowe Wydawnictwo Naukowe, Warsaw, 1967; Mir, Moscow, 1971).

    MATH  Google Scholar 

  19. G. E. Bredon, “Wilder manifolds are locally orientable,” Proc. Nat. Acad. Sci. USA 63(4), 1079–1081 (1969).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © D. V. Artamonov, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 5, pp. 643–659.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Artamonov, D.V. Local homology and dimensional full-valuedness. Math Notes 81, 573–589 (2007). https://doi.org/10.1134/S000143460705001X

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000143460705001X

Key words

Navigation