Advertisement

Mathematical Notes

, Volume 64, Issue 5, pp 607–615 | Cite as

Borel resolvability of compact spaces and their subspaces

  • V. I. Malykhin
Article

Abstract

The presence of disjoint dense (Borel) subsets in Tychonoff cubes, Borel subspaces of Tychonoff cubes, and dyadic compacta is examined. Several problems are stated.

Key words

resolvability of topological spaces, maximally, Borel Baire resolvable topological spaces, Borel,A-,GδFσ-sets in Tychonoff cubes,A-,CA-,PCACPCA-sets in compact spaces, dyadic compactum, perfectly normal compact space, Baire space, dispersion character 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Hewitt, “A problem of set-theoretic topology,”Duke Math. J.,10, 309–333 (1943).CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    M. Katetov, “On topological spaces containing no disjoint dense sets,”Mat. Sb. [Math. USSR-Sb.],21, No. 1, 3–12 (1947).MathSciNetGoogle Scholar
  3. 3.
    N. V. Veli¯cko, “On the theory of decomposable spaces,”Mat. Zametki [Math. Notes],19, No. 2, 209–214 (1976).MathSciNetGoogle Scholar
  4. 4.
    E. G. Pytkeev, “Maximally decomposable spaces,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],154, 209–213 (1983).MATHMathSciNetGoogle Scholar
  5. 5.
    W. W. Comfort and S. Garcia-Ferreira, “Resolvability: a selective survey and some new results,”Topology Appl.,74, 149–167 (1996).CrossRefMathSciNetGoogle Scholar
  6. 6.
    V. I. Malykhin, “Extremally disconnected and nearly extremally disconnected groups,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],220, No. 1, 27–30 (1975).MATHMathSciNetGoogle Scholar
  7. 7.
    W. W. Comfort and Mill J. van, “Groups with only resolvable group topologies,”Proc. Amer. Math. Soc.,120, 687–696 (1994).MathSciNetGoogle Scholar
  8. 8.
    J. Ceder, “On maximally Borel resolvable spaces,”Rev. Roumaine Math. Pures Appl.,11, 89–94 (1966).MATHMathSciNetGoogle Scholar
  9. 9.
    R. Jimenez and V. I. Malykhin, “Structure resolvability,”Comment. Math. Univ. Carolin.,39, No. 2, 379–388 (1998).MathSciNetGoogle Scholar
  10. 10.
    T. J. Jech,Lectures in Set Theory With Particular Emphasis on the Method of Forcing, Springer-Verlag, Berlin-Heidelberg-New York (1973).Google Scholar
  11. 11.
    B. A. Efimov, “Dyadic bicompacta,”Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.],14, 211–247 (1965).MathSciNetGoogle Scholar
  12. 12.
    V. I. Malykhin, “Maximal resolvability of bounded groups,”Mat. Zametki [Math. Notes] (to appear).Google Scholar
  13. 13.
    P. L. Sharma and S. Sharma, “Resolution properties in generalizedk-spaces,”Topology Appl.,29, 61–66 (1989).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. I. Malykhin
    • 1
  1. 1.S. Ordzhonikidze Moscow Academy of ManagementUSSR

Personalised recommendations