Countably perfectly meager sets

2020/10/17 by Pol, Roman, Zakrzewski, Piotr · 1 citation
#03E15 #03E20 #54E52 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2010.08812

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 ∈ \mathbb N\ of X, there exists an F_σ-set F in X such that A ⊆ F and F∩ 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 Bartoszyński.

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