Ideal limits of sequences of continuous functions
Tom 203 / 2009
Fundamenta Mathematicae 203 (2009), 39-46
MSC: 03E15, 28A20.
DOI: 10.4064/fm203-1-3
Streszczenie
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.
