Geodesic
Ideal limits of sequences of continuous functions
Miklós Laczkovich1 ; Ireneusz Recław2
1 Department of Analysis Eötvös Loránd University 1117 Budapest, Hungary and Department of Mathematics University College London London, UK
2 Institute of Informatics University of Gdańsk 80-952 Gdańsk, Poland
Fundamenta Mathematicae, Tome 203 (2009) no. 1, pp. 39-46

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm203-1-3
Keywords: prove every borel ideal ideal limits sequences continuous functions polish space baire class only ideal does contain copy hbox fin times hbox fin particular sigma delta ideals proof borel determinacy game introduced laflamme

Miklós Laczkovich 1 ; Ireneusz Recław 2

1 Department of Analysis Eötvös Loránd University 1117 Budapest, Hungary and Department of Mathematics University College London London, UK
2 Institute of Informatics University of Gdańsk 80-952 Gdańsk, Poland 
@article{10_4064_fm203_1_3,
     author = {Mikl\'os Laczkovich and Ireneusz Rec{\l}aw},
     title = {Ideal limits of sequences of continuous functions},
     journal = {Fundamenta Mathematicae},
     pages = {39--46},
     publisher = {mathdoc},
     volume = {203},
     number = {1},
     year = {2009},
     doi = {10.4064/fm203-1-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm203-1-3/}
}
TY  - JOUR
AU  - Miklós Laczkovich
AU  - Ireneusz Recław
TI  - Ideal limits of sequences of continuous functions
JO  - Fundamenta Mathematicae
PY  - 2009
SP  - 39
EP  - 46
VL  - 203
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm203-1-3/
DO  - 10.4064/fm203-1-3
LA  - en
ID  - 10_4064_fm203_1_3
ER  - 
%0 Journal Article
%A Miklós Laczkovich
%A Ireneusz Recław
%T Ideal limits of sequences of continuous functions
%J Fundamenta Mathematicae
%D 2009
%P 39-46
%V 203
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm203-1-3/
%R 10.4064/fm203-1-3
%G en
%F 10_4064_fm203_1_3
Miklós Laczkovich; Ireneusz Recław. Ideal limits of sequences of continuous functions. Fundamenta Mathematicae, Tome 203 (2009) no. 1, pp. 39-46. doi: 10.4064/fm203-1-3

Cité par Sources :