Ideal limits of sequences of continuous functions

Volume 203 / 2009

Miklós Laczkovich, Ireneusz Recław Fundamenta Mathematicae 203 (2009), 39-46 MSC: 03E15, 28A20. DOI: 10.4064/fm203-1-3


We prove that for every Borel ideal, the ideal limits of sequences of continuous functions on a Polish space are of Baire class one if and only if the ideal does not contain a copy of $\hbox {Fin}\times \hbox {Fin}.$ In particular, this is true for $F_{\sigma \delta }$ ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme.


  • Miklós LaczkovichDepartment of Analysis
    Eötvös Loránd University
    1117 Budapest, Hungary
    Department of Mathematics
    University College London
    London, UK
  • Ireneusz RecławInstitute of Informatics
    University of Gdańsk
    80-952 Gdańsk, Poland

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