Filters and sequences

Sławomir Solecki

ArticleOriginal scientific text

Title

Filters and sequences

Authors ¹

Affiliations

Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.

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.

Keywords

ENG

filters, separation property, Fatou's lemma

[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.
[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.
[M] K. Mazur, $F_{σ}$ -ideals and $ω_{1} ω_{1}^{\cdot}$ -gaps in the Boolean algebra P(ω)/I, Fund. Math. 138 (1991), 103-111.
[R] H. L. Royden, Real Analysis, Macmillan, 1988.

Title

Filters and sequences

Affiliations

Abstract

Keywords

Bibliography