Skip to main content
SpringerLink
Log in

On the difference property of the family of functions with the Baire property

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We show that it is consistent with ZFC that the family of functions with the Baire property has the difference property. That is, every function for which f(x + h)-f(x) has the Baire property for every h∈R is of the form f=g + Awhere g has the Baire property and A is additive.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. G. de Bruijn, Functions whose differences belong to a given class, Nieuw Arch. Wisk., 23 (1951), 194–218.

    MATH  MathSciNet  Google Scholar 

  2. J. Cichoń, A. Kharazishvili and B. Weglorz, Subsets of the Real Line, Łódź University Press (Łódź, 1995).

    Google Scholar 

  3. M. Kada and Y. Yuasa, Cardinal invariants about shrinkability of unbounded sets, Topology Appl., 74 (1996), 215–223.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Komjáth, Some remarks on second category sets, Colloq. Math., 66 (1993), 57–62.

    MATH  MathSciNet  Google Scholar 

  5. M. Laczkovich, Two constructions of Sierpiński and some cardinal invariants of ideals, Real Anal. Exchange, 24 (1998/99), 663–676.

    MATH  MathSciNet  Google Scholar 

  6. M. Laczkovich, The difference property, in: Paul Erdős and His Mathematics (G. Halász, L. Lovász, M. Simonovits and V. T. Sós, eds.), Bolyai Society Math. Studies, 11 (Budapest, 2002), pp. 363–410.

  7. T. Mátrai, Weak difference property of functions with the Baire property, manuscript.

  8. I. Recław, On the double difference property for functions with Baire property, submitted to Acta Math. Hungar.

  9. I. Recław and P. Zakrzewski, Strong Fubini properties of ideals, Fund. Math., 159 (1999), 135–152.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Polish Academy of Sciences Abrahama 18, Institute of Mathematics, 81-825, Sopot, Poland

    R. Filipów

Authors
  1. R. Filipów
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Filipów, R. On the difference property of the family of functions with the Baire property. Acta Mathematica Hungarica 100, 97–104 (2003). https://doi.org/10.1023/A:1024608301864

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024608301864

Search

Navigation