Ideal limits of sequences of continuous functions

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 -