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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 closedHaar-meager sets. This example is applied to studying the interplay betweenvarious classes of ``large'' sets and Kuczma--Ger classes in the topologicalvector spaces $\mathbb R^n$ for $n\le \omega$.

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