Journal of Symbolic Logic

Ideal convergence of bounded sequences

Rafał Filipów, Recław Ireneusz, Mrożek Nikodem, and Szuca Piotr

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergent subsequence) on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.

Article information

Source
J. Symbolic Logic Volume 72, Issue 2 (2007), 501-512.

Dates
First available in Project Euclid: 30 July 2007

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1185803621

Digital Object Identifier
doi:10.2178/jsl/1185803621

Mathematical Reviews number (MathSciNet)
MR2320288

Zentralblatt MATH identifier
1123.40002

Subjects
Primary: 40A05: Convergence and divergence of series and sequences
Secondary: 26A03: Foundations: limits and generalizations, elementary topology of the line 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)

Keywords
Bolzano-Weierstrass property Bolzano-Weierstrass theorem statistical density statistical convergence ideal convergence filter convergence subsequence extending ideals P-ideals P-points analytic ideals maximal ideals

Citation

Filipów, Rafał; Nikodem, Mrożek; Ireneusz, Recław; Piotr, Szuca. Ideal convergence of bounded sequences. J. Symbolic Logic 72 (2007), no. 2, 501--512. doi:10.2178/jsl/1185803621. http://projecteuclid.org/euclid.jsl/1185803621.


Export citation