Skip to main content
Log in

Functions of the first Baire class with values in metrizable spaces

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We show that every mapping of the first functional Lebesgue class that acts from a topological space into a separable metrizable space that is linearly connected and locally linearly connected belongs to the first Baire class. We prove that the uniform limit of functions of the first Baire class ƒ n: XY belongs to the first Baire class if X is a topological space and Y is a metric space that is linearly connected and locally linearly connected.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. R. W. Hansell, “Borel measurable mappings for nonseparable metric spaces,” Trans. Amer. Math. Soc., 161, 145–169 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  2. R. W. Hansell, “Extended Bochner measurable selectors,” Math. Ann., 277, 79–94 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  3. K. Kuratowski, Topology [Russian translation], Vol. 1, Mir, Moscow (1966).

    Google Scholar 

  4. O. O. Karlova, “First functional Lebesgue class and Baire classification of separately continuous mappings,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 191/192, 52–60 (2004).

  5. R. W. Hansell, “Lebesgue’s theorem on Baire class 1 functions,” in: Topology with Applications, Szekszard, Hungary (1993), pp. 251–257.

  6. O. O. Karlova, “Baire classification of mappings with values in subsets of finite-dimensional spaces, ” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 239, 59–65 (2005).

  7. M. Fosgerau, “When are Borel functions Baire functions?,” Fund. Math., 143, 137–152 (1993).

    MATH  MathSciNet  Google Scholar 

  8. W. F. Osgood, “Ueber die ungleichmäßige Convergenz und die gliedweise Integration der Reihen,” Nachr. Ges. Wiss. Göttingen, 288–291 (1896).

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 568–572, April, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karlova, O.O., Mykhailyuk, V.V. Functions of the first Baire class with values in metrizable spaces. Ukr Math J 58, 640–644 (2006). https://doi.org/10.1007/s11253-006-0089-2

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0089-2

Keywords

Navigation