Siberian Mathematical Journal

, Volume 59, Issue 6, pp 1006–1013 | Cite as

A Complete Topological Classification of the Space of Baire Functions on Ordinals

  • L. V. Genze
  • S. P. Gulko
  • T. E. Khmyleva


Considering the spaces Bp[1, α] of all Baire functions x: [1, α] → ℝ on the ordinal segments [1, α] that are endowed with the topology of pointwise convergence, we give a complete topological classification of these spaces.


Baire 1-function space of Baire functions topology of pointwise convergence homeomorphism ordinal segment order topology real compactness 


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  1. 1.
    Bessaga C. and Pe–lczýnski A., “On isomorphic classification of spaces of continuous functions,” Studia Math., vol. 19, No. 1, 53–62 (1960).MathSciNetCrossRefGoogle Scholar
  2. 2.
    Semadeni Z., “Banach spaces non-isomorphic to their Cartesian squares. II,” Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys., vol. 8, No. 2, 81–84 (1960).MathSciNetzbMATHGoogle Scholar
  3. 3.
    Gulko S. P. and Oskin A. V., “Isomorphic classification of spaces of continuous functions on totally ordered compact sets,” Funct. Anal. Appl., vol. 9, No. 1, 56–57 (1975).CrossRefGoogle Scholar
  4. 4.
    Kislyakov V. E., “Classification of spaces of continuous functions of ordinals,” Sib. Math. J., vol. 16, No. 2, 226–231 (1975).MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gulko S. P., “Free topological groups and spaces of continuous functions on ordinals,” Vestn. Tomsk Gos. Univ., no. 280, 34–38 (2003).Google Scholar
  6. 6.
    Baars J. and de Groot J., On Topological and Linear Equivalence of Certain Function Spaces, Centre Math. Comput. Sci., Amsterdam (1992) (CWI Tract; vol. 86).Google Scholar
  7. 7.
    Genze L. V., Gulko S. P., and Khmyleva T. E., “Classification of spaces of Baire functions on ordinal intervals,” Trudy Inst. Mat. i Mekh. UrO RAN, vol. 16, No. 3, 61–66 (2010).Google Scholar
  8. 8.
    Engelking R., General Topology, Heldermann Verlag, Berlin (1989).zbMATHGoogle Scholar
  9. 9.
    Arkhangelskii A. V., “Linear homeomorphisms of function spaces,” Soviet Math. Dokl., vol. 25, No. 6, 852–855 (1982).MathSciNetGoogle Scholar
  10. 10.
    Tkachuk V. V., A Cp-Theory Problem Book. Topological and Function Spaces, Springer-Verlag, New York (2011).CrossRefzbMATHGoogle Scholar
  11. 11.
    Arkhangelskii A. V., Topological Function Spaces [Russian], Moscow Univ., Moscow (1989).Google Scholar
  12. 12.
    Gulko S. P., “Spaces of continuous functions on ordinals and ultrafilters,” Math. Notes, vol. 47, No. 4, 329–334 (1990).MathSciNetCrossRefGoogle Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Tomsk State UniversityTomskRussia

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