Geodesic
Filters and sequences
Fundamenta Mathematicae, Tome 163 (2000) no. 3, pp. 215-228.

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

We consider two situations which relate properties of filters with properties of the limit operators with respect to these filters. In the first one, we show that the space of sequences having limits with respect to a $Π^0_3$ filter is itself $Π^0_3$ and therefore, by a result of Dobrowolski and Marciszewski, such spaces are topologically indistinguishable. This answers a question of Dobrowolski and Marciszewski. In the second one, we characterize universally measurable filters which fulfill Fatou's lemma.
DOI : 10.4064/fm-163-3-215-228
Keywords: filters, separation property, Fatou's lemma

Sławomir Solecki 1

1 
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Sławomir Solecki. Filters and sequences. Fundamenta Mathematicae, Tome 163 (2000) no. 3, pp. 215-228. doi : 10.4064/fm-163-3-215-228. http://geodesic.mathdoc.fr/articles/10.4064/fm-163-3-215-228/

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