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Linear homeomorphisms of spaces of continuous functions on long Sorgenfrey lines

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Abstract

We carry out a linear homeomorphic classification of the spaces of continuous functions on the long Sorgenfrey lines S α, where a is an arbitrary ordinal. The spaces of continuous functions are endowed with the topology of pointwise convergence and denoted by C p (S α).

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References

  1. Bessaga C. and Pełczyński C., “On isomorphic classification of spaces of continuous functions,” Studia Math., 19, 53–62 (1960).

    MathSciNet  MATH  Google Scholar 

  2. Semadeni Z., “Banach spaces non-isomorphic to their Cartesian squares. II,” Bull. Acad. Pol. Sci. Ser. Math. Astronom. Phys., 8, 81–84 (1960).

    MathSciNet  MATH  Google Scholar 

  3. Gul’ko S. P. and Os’kin A. V., “Isomorphic classification of spaces of continuous functions on totally ordered compact sets,” Funct. Anal. Appl., 9, No. 1, 56–57 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  4. Kislyakov V. E., “Classification of spaces of continuous functions of ordinals,” Sib. Math. J., 16, No. 2, 226–231 (1975).

    Article  MathSciNet  Google Scholar 

  5. Engelking R., General Topology, Heldermann Verlag, Berlin (1989).

    MATH  Google Scholar 

  6. Fedorchuk V. V., “Bicompacta with noncoinciding dimensionalities,” Soviet Math. Dokl., 182, No. 2, 1148–1150 (1968).

    MathSciNet  MATH  Google Scholar 

  7. Burke D. K. and Moore J. T., “Subspaces of the Sorgenfrey line,” Topology Appl., 90, 57–68 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  8. Arkhangel’skiĭ A. V., Topological Function Spaces [in Russian], Moscow Univ., Moscow (1989).

    Google Scholar 

  9. Arkhangel’skiĭ A. V., “On linear homomorphisms of function spaces,” Dokl. Akad. Nauk SSSR, 264, No. 6, 1289–1292 (1982).

    MathSciNet  Google Scholar 

  10. Kuratowski K. and Mostowski A., Theory of Sets [Russian translation], Mir, Moscow (1970).

    MATH  Google Scholar 

  11. Gul’ko S. P., “Free topological groups and spaces of continuous functions on ordinals,” Vestn. Tomsk Gos. Univ., No. 280, 34–38 (2003).

    Google Scholar 

  12. Pełczyński A., Linear Extensions, Linear Averagings, and Their Applications to Linear Topological Classification of Spaces of Continuous Functions [Russian translation], Mir, Moscow (1979).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Tomsk State University, Tomsk, Russia

    N. N. Trofimenko & T. E. Khmyleva

Authors
  1. N. N. Trofimenko
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  2. T. E. Khmyleva
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Correspondence to N. N. Trofimenko.

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Tomsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 3, pp. 709–717, May–June, 2016; DOI: 10.17377/smzh.2016.57.320.

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Trofimenko, N.N., Khmyleva, T.E. Linear homeomorphisms of spaces of continuous functions on long Sorgenfrey lines. Sib Math J 57, 558–564 (2016). https://doi.org/10.1134/S0037446616030204

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  • DOI: https://doi.org/10.1134/S0037446616030204

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