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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 Fin × Fin. In particular, this is true for ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme.
Miklós Laczkovich, and Ireneusz Recław. "Ideal limits of sequences of continuous functions." Fundamenta Mathematicae 203.1 (2009): 39-46. <http://eudml.org/doc/282831>.
@article{MiklósLaczkovich2009, abstract = {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 Fin × Fin. In particular, this is true for $F_\{σδ\}$ ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme.}, author = {Miklós Laczkovich, Ireneusz Recław}, journal = {Fundamenta Mathematicae}, keywords = {ideal convergence; infinite games; Baire class one}, language = {eng}, number = {1}, pages = {39-46}, title = {Ideal limits of sequences of continuous functions}, url = {http://eudml.org/doc/282831}, volume = {203}, year = {2009}, }
TY - JOUR AU - Miklós Laczkovich AU - Ireneusz Recław TI - Ideal limits of sequences of continuous functions JO - Fundamenta Mathematicae PY - 2009 VL - 203 IS - 1 SP - 39 EP - 46 AB - 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 Fin × Fin. In particular, this is true for $F_{σδ}$ ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme. LA - eng KW - ideal convergence; infinite games; Baire class one UR - http://eudml.org/doc/282831 ER -