Abstract
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 Π03 filter is itself Π03 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 215-228 |
| Number of pages | 14 |
| Journal | Fundamenta Mathematicae |
| Volume | 163 |
| Issue number | 3 |
| State | Published - 2000 |
| Externally published | Yes |
Keywords
- Fatou's lemma
- Filters
- Separation property
ASJC Scopus subject areas
- Algebra and Number Theory