Ideal convergence of bounded sequences
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- J. Symb. Log.
دوره 72 شماره
صفحات -
تاریخ انتشار 2007