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

英文摘要：

We prove that the countable product of lines contains a Borel linear subspace $L\ne\mathbb R^ω$ 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 $\mathbb R^n$ for $n\le ω$.