Translator Disclaimer
June 2007 Ideal convergence of bounded sequences
Rafał Filipów, Recław Ireneusz, Mrożek Nikodem, Szuca Piotr
J. Symbolic Logic 72(2): 501-512 (June 2007). DOI: 10.2178/jsl/1185803621

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.

Citation

Download Citation

Rafał Filipów. Recław Ireneusz. Mrożek Nikodem. Szuca Piotr. "Ideal convergence of bounded sequences." J. Symbolic Logic 72 (2) 501 - 512, June 2007. https://doi.org/10.2178/jsl/1185803621

Information

Published: June 2007
First available in Project Euclid: 30 July 2007

zbMATH: 1123.40002
MathSciNet: MR2320288
Digital Object Identifier: 10.2178/jsl/1185803621

Subjects:
Primary: 40A05
Secondary: 26A03 , 54A20

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

Rights: Copyright © 2007 Association for Symbolic Logic

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.72 • No. 2 • June 2007
Back to Top