Skip to main content
SpringerLink
Log in

On finite-dimensional nonmetrizable manifolds

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. P. S. Alexandroff, “On local properties of closed sets,”Ann. Math.,26, 1–35 (1935).

    MathSciNet  Google Scholar 

  2. P. S. Alexandroff,Introduction to Homological Dimension Theory [In Russian], Nauka, Moscow ( (1975).

    Google Scholar 

  3. P. S. Alexandroff and B. A. Pasynkov,Introduction to Dimension Theory [In Russian], Nauka, Moscow (1973).

    Google Scholar 

  4. R. D. Anderson, “Monotone interior dimension raising mappings,”Duke Math. J.,19, 359–366 (1952).

    MATH  MathSciNet  Google Scholar 

  5. Z. Balogh, “Locally nice spaces under Martin's Axiom,”Comment. Math. Univ. Carolinae,24, 63–87 (1983).

    MATH  MathSciNet  Google Scholar 

  6. R. H. Bing, “The cartesian product of a certain nonmanifold and a line isE 4,”Ann. Math.,70, 399–412 (1959).

    MATH  MathSciNet  Google Scholar 

  7. M. Brown, “Some application of an approximation theorem for inverse limits,”Proc. Amer. Math. Soc.,11, 478–483 (1960).

    MATH  MathSciNet  Google Scholar 

  8. M. Brown, “The monotone union of openn-cells is an openn-cell,”Proc. Amer. Math. Soc.,12, 812–814 (1961).

    MATH  MathSciNet  Google Scholar 

  9. T. A. Chapman,Lectures on Hilbert Cube Manifolds, CBMS,28, AMS, Providence (1976).

    Google Scholar 

  10. C. H. Dowker, “On countably paracompact spaces,”Canad. J. Math.,3, 219–224 (1941).

    MathSciNet  Google Scholar 

  11. C. H. Dowker, “Local dimension of normal spaces,”Quart. J. Math. Ser. 2,6, No. 22, 101–120 (1955).

    MATH  MathSciNet  Google Scholar 

  12. R. Engelking,General Topology, PWN, Warszawa (1977).

    Google Scholar 

  13. R. Engelking,Dimension Theory, PWN, Warszawa (1978).

    Google Scholar 

  14. V. V. Fedorchuk, “Mappings that do not reduce dimension,”Dokl. Akad. Nauk SSSR,185, No. 1, 54–57 (1969).

    MATH  MathSciNet  Google Scholar 

  15. V. V. Fedorchuk, “Fully closed maps, scannable spectra and cardinality of hereditarily separable spaces,”General Topol. Appl.,10, 247–274 (1979).

    MATH  MathSciNet  Google Scholar 

  16. V. V. Fedorchuk,Products and Spectra of Topological Spaces. Part II [In Russian], MGU, Moscow (1980).

    Google Scholar 

  17. V. V. Fedorchuk, “On the dimension of nowhere dense subsets of manifolds,”Vestn. Mosk. Univ., Mat., Mekh., No. 2, 23–28 (1992).

    MATH  MathSciNet  Google Scholar 

  18. V. V. Fedorchuk, “On the dimension of non-metrizable manifolds,” In:Workshop on Gener. Topol. and Geom. Topol. 1991, Univ. of Tsukuba (1992), pp. 35–66.

  19. V. V. Fedorchuk, “On differentiable manifolds with noncoinciding dimensions,”Topol. Appl.,48 (1993).

  20. V. V. Fedorchuk, “A differentiable manifold with noncoinciding dimensions under CH,”Math. Express,1 (1993).

  21. V. V. Fedorchuk and V. V. Filippov, “Manifolds with noncoinciding inductive dimensions,”Mat. Sb.,183, No. 9, 29–44 (1992).

    Google Scholar 

  22. W. G. Fleissner, “Normal Moore spaces in the constructible universe,”Proc. Amer. Math. Soc.,46, 294–298 (1974).

    MATH  MathSciNet  Google Scholar 

  23. W. G. Fleissner, “The normal Moore space conjecture and large cardinals,” In:Handbook of Set-Theoretic Topology, North Holland, Amsterdam (1984), pp. 733–760.

    Google Scholar 

  24. K. Gödel,The Consistency of the Axiom of Choice and of the Generalized Continuum Hypotheses, Princeton (1940).

  25. H. Grauert, “On Levi's problem and the imbedding of real-analytic manifolds,”Ann. Math.,68, 460–472 (1958).

    MATH  MathSciNet  Google Scholar 

  26. R. E. Hodel, “The number of metrizable spaces,”Fundam. Math.,115, No. 2, 127–141 (1983).

    MATH  MathSciNet  Google Scholar 

  27. T. J. Jech,Lectures in Set Theory with Particular Emphasis on the Method of Forcing, Springer-Verlag (1971).

  28. R. B. Jensen, “The fine structure of the constructible hierarchy,”Ann. Math. Logic,4 229–308 (1972).

    Article  MATH  MathSciNet  Google Scholar 

  29. W. Koch and D. Puppe, “Differenzierbare Structuren auf Manigfaltigkeiten ohne abzahlbare Basis,”Arc. Math.,19, 95–102 (1968).

    MathSciNet  Google Scholar 

  30. G. Kozlowski and P. Zenor, “A differentiable perfectly normal nonmetrizable manifold,”Topology Proc.,4, 453–460 (1979).

    MathSciNet  Google Scholar 

  31. K. Kunen,Set Theory. An Introduction to Independence Proofs, Studies in Logic and the Foundation of Math. 102, North Holland, Amsterdam (1980).

    Google Scholar 

  32. R. L. Moore, “Concerning separability,”Proc. Nat. Acad. Sci. USA,28, 56–58 (1942).

    MATH  Google Scholar 

  33. J. Nagata,Modern Dimension Theory, Groningen 91965).

  34. P. J. Nyikos, “Set-theoretic topology of manifolds,” In:Proc. of the Fifth Prague Topol. Symp., Helderman Ferlag, Praha (1983), pp. 513–526.

    Google Scholar 

  35. P. J. Nyikos, “The theory of nonmetrizable manifolds.” In:Handbook of Set-Theoretic Topology, North Holland, Amsterdam (1984), pp. 633–684.

    Google Scholar 

  36. P. J. Nyikos, “On first countable, countably compact spaces III: The problem of obtaining separable noncompact examples,” In:Open problems in Topology, North Holland, Amsterdam (1990), pp. 127–161.

    Google Scholar 

  37. A. J. Ostaszewski, “On countably compact perfectly normal spaces”J. London Math. Soc.,14, 505–516 (1976).

    MATH  MathSciNet  Google Scholar 

  38. M. M. Postnikov,Smooth Manifolds [In Russian], Nauka, Moscow (1987).

    Google Scholar 

  39. G. M. Reed and P. Zenor, “Metrization of Moore spaces and generalized manifolds,”Fundam. Math.,91, 203–209 (1976).

    MathSciNet  Google Scholar 

  40. M. E. Rudin, “The undecidability of the existence of a perfectly normal nonmetrizable manifold,”Houston J. Math.,5, 249–252 (1979).

    MATH  MathSciNet  Google Scholar 

  41. M. E. Rudin, “Countable, point separating open covers for manifolds,”Houston J. Math.,15, 255–266 (1989).

    MATH  MathSciNet  Google Scholar 

  42. M. E. Rudin, “Some conjectures,” In:Open Problems in Topology, North Holland, Amsterdam (1990), pp. 83–193.

    Google Scholar 

  43. M. E. Rudin, “Two nonmetrizable manifolds,”Topol Appl., (1990).

  44. M. E. Rudin and P. Zenor, “A perfectly normal nonmetrizable manifold,”Houston J. Math.,2, 129–134 (1976).

    MathSciNet  Google Scholar 

  45. N. V. Savinov, “On completely closed mappings,”Vestn. Mosk. Univ., Mat., Mekh., No. 4, 39–45 (1975).

    MATH  MathSciNet  Google Scholar 

  46. E. G. Sklyarenko, “On some applications of sheaf theory to general topology,”Uspekhi Mat. Nauk,19, No. 6, 47–70 (1964).

    MATH  MathSciNet  Google Scholar 

  47. J. E. Vaughan, “Small uncountable cardinals and topology,” In:Open Problems in Topology, North Holland, Amsterdam (1990), pp. 196–216.

    Google Scholar 

  48. H. Whitney, “Differentiable manifolds,”Ann. Math.,37, 645–680 (1936).

    MATH  MathSciNet  Google Scholar 

  49. H. H. Wicke and J. M. Worrell “Characterization of developable topological spaces,”Canad. J. Math.,17, 820–830 (1965).

    MathSciNet  Google Scholar 

Download references

Authors
  1. V. V. Fedorchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The survey is devoted to the theory of nonmetrizable manifolds. The basic constructions and concepts are considered, and major attention is given to the dimension theory of manifolds.

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie, Obzory. Vol. 6, Topologiya-1, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fedorchuk, V.V. On finite-dimensional nonmetrizable manifolds. J Math Sci 74, 813–833 (1995). https://doi.org/10.1007/BF02362844

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02362844

Keywords

Search

Navigation