Filters and sequences

• Autorzy: Sławomir Solecki
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

filters; separation property; Fatou's lemma

Kategorie tematyczne

• 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
• 54C35: Function spaces
• 03E15: Descriptive set theory
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 163
• Numer: 3
• Strony: 215-228

Daty

wydano

2000

otrzymano

1999-01-11

poprawiono

1999-09-21

Twórcy

autor

Sławomir Solecki

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

Bibliografia

• [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 $ω_1ω_1^*$-gaps in the Boolean algebra P(ω)/I, Fund. Math. 138 (1991), 103-111.
• [R] H. L. Royden, Real Analysis, Macmillan, 1988.