# Filters and sequences

Fundamenta Mathematicae (2000)

- Volume: 163, Issue: 3, page 215-228
- ISSN: 0016-2736

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topSolecki, Sławomir. "Filters and sequences." Fundamenta Mathematicae 163.3 (2000): 215-228. <http://eudml.org/doc/212440>.

@article{Solecki2000,

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 $Π^0_3$ 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.},

author = {Solecki, Sławomir},

journal = {Fundamenta Mathematicae},

keywords = {filters; separation property; Fatou's lemma},

language = {eng},

number = {3},

pages = {215-228},

title = {Filters and sequences},

url = {http://eudml.org/doc/212440},

volume = {163},

year = {2000},

}

TY - JOUR

AU - Solecki, Sławomir

TI - Filters and sequences

JO - Fundamenta Mathematicae

PY - 2000

VL - 163

IS - 3

SP - 215

EP - 228

AB - 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.

LA - eng

KW - filters; separation property; Fatou's lemma

UR - http://eudml.org/doc/212440

ER -

## References

top- [DM] T. Dobrowolski and W. Marciszewski, Classification of function spaces with the pointwise topology determined by a countable dense set, Fund. Math. 148 (1995), 35-62. Zbl0834.46016
- [K] A. S. Kechris, Classical Descriptive Set Theory, Springer, 1995.
- [L] A. Louveau, Sur la génération des fonctions boréliennes fortement affines sur un convexe compact métrisable, Ann. Inst. Fourier (Grenoble) 36 (1986), no. 2, 57-68. Zbl0604.46012
- [M] K. Mazur, ${F}_{\sigma}$-ideals and ${\omega}_{1}{\omega}_{1}^{*}$-gaps in the Boolean algebra P(ω)/I, Fund. Math. 138 (1991), 103-111.
- [R] H. L. Royden, Real Analysis, Macmillan, 1988. Zbl0704.26006

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