Countably perfectly meager sets

Roman Pol; Piotr Zakrzewski

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arXiv · 2010.08812

Countably perfectly meager sets

Roman Pol·Piotr Zakrzewski

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Abstract

We study a strengthening of the notion of a perfectly meager set. We say that that a subset $A$ of a perfect Polish space $X$ is countably perfectly meager in $X$, if for every sequence of perfect subsets $\{P_n: n \in {\mathbb N}\}$ of $X$, there exists an $F_\sigma$-set $F$ in $X$ such that $A \subseteq F$ and $F\cap P_n$ is meager in $P_n$ for each $n$. We give various characterizations and examples of countably perfectly meager sets. We prove that not every universally meager set is countably perfectly meager correcting an earlier result of Bartoszy\'nski.

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BibTeX RIS

Roman Pol, Piotr Zakrzewski. 2020-10-17. Countably perfectly meager sets. https://arxiv.org/abs/2010.08812

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