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A Borel linear subspace of $\mathbb R^ω$ that cannot be covered by countably many closed Haar-meager sets (2201.02888v1)

Published 8 Jan 2022 in math.FA and math.GN

Abstract: We prove that the countable product of lines contains a Borel linear subspace $L\ne\mathbb R\omega$ that cannot be covered by countably many closed Haar-meager sets. This example is applied to studying the interplay between various classes of ``large'' sets and Kuczma--Ger classes in the topological vector spaces $\mathbb Rn$ for $n\le \omega$.

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