Ideal convergence of bounded sequences

We generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergentsubsequence) on ideal convergence. Weshow examplesofidealswith and without the BolzanoWeierstrass 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.

• Type: Journal
• Year: 2007
• Where: JSYML
• Authors: Rafal Filipów, Reclaw Ireneusz, Mrozek Nikodem, Piotr Szuca
• Keywords: Boolean Algebra, Bounded Sequence, BW Property, JSYML 2007