Advertisement

Siberian Mathematical Journal

, Volume 54, Issue 3, pp 388–392 | Cite as

On the spectral height of F-compact spaces

  • M. A. BaranovaEmail author
  • A. V. Ivanov
Article

Abstract

We prove that given an ordinal α with 0 < αω 1 and αβ+1, where β is a limit ordinal, there exists an F-compact space of spectral height α.

Keywords

fully closed mapping resolution F-compact space spectral height 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ivanov A. V., “On Fedorchuk’s bicompacta,” in: Mappings and Functors [in Russian], Moscow Univ., Moscow, 1984, pp. 31–40.Google Scholar
  2. 2.
    Watson S., “The construction of topological spaces: Planks and resolutions,” in: Recent Progress in General Topology, North-Holland, Amsterdam, 1992, pp. 673–757.Google Scholar
  3. 3.
    Fedorchuk V. V., “Fully closed mappings and their applications,” J. Math. Sci. (New York), 136, No. 5, 4201–4292 (2006).MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ivanov A. V. and Kashuba E. V., “Hereditary normality of a space of the form F (X),” Siberian Math. J., 49, No. 4, 650–659 (2008).MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ivanov A. V. and Osipov E. V., “Degree of discrete generation of compact sets,” Math. Notes, 87, No. 3, 367–371 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Ivanov A. V., “A generalization of Gruenhage’s example,” Topology Appl., 157, No. 3, 517–525 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Fedorchuk V. V., “Fully closed maps, scannable spectra and cardinality of hereditarily separable spaces,” Gen. Topology Appl., 10, No. 3, 247–274 (1979).MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Ivanov A. V., “Hereditary normality of F-bicompacta,” Math. Notes, 39, No. 4, 332–334 (1986).zbMATHCrossRefGoogle Scholar
  9. 9.
    Fedorchuk V. V., “Bicompacta with noncoinciding dimensionalities,” Soviet Math., Dokl., 9, 1148–1150 (1968).zbMATHGoogle Scholar
  10. 10.
    Aleksandroff P. S. and Pasynkov B. A., Introduction to Dimension Theory [in Russian], Nauka, Moscow (1973).Google Scholar
  11. 11.
    Fedorchuk V. V., “A compact Hausdorff space all of whose infinite closed subsets are n-dimensional,” Math. USSR-Sb., 25, No. 1, 37–57 (1975).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Petrozavodsk State UniversityPetrozavodskRussia

Personalised recommendations