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

2022/01/08 by Тарас Банах, Banakh, Taras, Eliza Jabłońska +1
Computer Science · Mathematics · #28C10 #46A03 #54C30 #54H05 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2201.02888

openalex publication_date 2022/01/08 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We prove that the countable product of lines contains a Borel linear subspace L≠\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 Rⁿ for n≤ ω.

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