We show that an ideal I on the positive integers is meager if and only if there exists a bounded nonconvergent real sequence x such that the set of subsequences [resp. permutations] of x which preserve the set of I-limit points is comeager and, in addition, every accumulation point of x is also an I-limit point (that is, a limit of a subsequence (x n k ) such that {n1, n2, . . . , } /∈ I). The analogous characterization holds also for I-cluster points.

Another characterization of meager ideals

Paolo Leonetti
2023-01-01

Abstract

We show that an ideal I on the positive integers is meager if and only if there exists a bounded nonconvergent real sequence x such that the set of subsequences [resp. permutations] of x which preserve the set of I-limit points is comeager and, in addition, every accumulation point of x is also an I-limit point (that is, a limit of a subsequence (x n k ) such that {n1, n2, . . . , } /∈ I). The analogous characterization holds also for I-cluster points.
2023
2023
https://link.springer.com/article/10.1007/s13398-023-01423-9
Ideal limit point; Ideal cluster point; Meager ideal; Subsequences; Permutations
Balcerzak, Marek; Glab, Szymon; Leonetti, Paolo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2163271
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