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arXiv · 2109.05266

Another characterization of meager ideals

Marek Balcerzak·Szymon Glab·Paolo Leonetti
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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.

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Marek Balcerzak, Szymon Glab, Paolo Leonetti. 2021-09-11. Another characterization of meager ideals. https://arxiv.org/abs/2109.05266

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