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

Taras Banakh; Eliza Jabłońska

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

Functional Analysis 2022-01-11 v1 General Topology

Authors: Taras Banakh , Eliza Jabłońska

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 $\mathbb R^n$ for $n\le \omega$ .

Keywords

borel linear subspace haar-meager sets countable product of lines topological vector space kuczma-ger classes large sets

Cite

@article{arxiv.2201.02888,
  title  = {A Borel linear subspace of $\mathbb R^\omega$ that cannot be covered by countably many closed Haar-meager sets},
  author = {Taras Banakh and Eliza Jabłońska},
  journal= {arXiv preprint arXiv:2201.02888},
  year   = {2022}
}

Comments

9 pages. arXiv admin note: text overlap with arXiv:1803.06712

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

Abstract

Keywords

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