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arXiv · 2606.03366

Everywhere $\mathcal{I}$ sets

Jakub Cieplechowicz·Szymon Żeberski
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Abstract

Let $\mathcal{I}$ be a $\sigma$-ideal on the Cantor space $2^{\omega}$. A set $X\subseteq 2^\omega$ is called everywhere $\mathcal{I}$ if for any $S\in [\omega]^\omega$ the set $X\!\restriction\! S\in\mathcal{I}(2^S).$ We will discuss relations between such families in the class of perfect and Borel sets.

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Jakub Cieplechowicz, Szymon Żeberski. 2026-06-02. Everywhere $\mathcal{I}$ sets. https://doi.org/10.1016/j.topol.2026.109919

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