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

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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. Filters and sequences. Fundamenta Mathematicae, Tome 163 (2000) no. 3, pp. 215-228. doi: 10.4064/fm-163-3-215-228
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