Another characterization of meager ideals
Abstract
We show that an ideal $\mathcal{I}$ 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 $\mathcal{I}$limit points is comeager and, in addition, every accumulation point of $x$ is also an $\mathcal{I}$limit point (that is, a limit of a subsequence $(x_{n_k})$ such that $\{n_1,n_2,\ldots,\} \notin \mathcal{I}$). The analogous characterization holds also for $\mathcal{I}$cluster points.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.05266
 Bibcode:
 2021arXiv210905266B
 Keywords:

 Mathematics  General Topology;
 Mathematics  Functional Analysis
 EPrint:
 10pp