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

Object's details: A Borel linear subspace of R^\omega that cannot be covered by countably many closed Haar-meager sets

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Provider:Akademicka Platforma Czasopism

Description

Title:
A Borel linear subspace of R^\omega that cannot be covered by countably many closed Haar-meager sets
Creator:
Banakh, Taras;
Jabłońska, Eliza
Description:
We prove that the countable product of lines contains a Haar-null Haar-meager Borel linear subspace $L$ 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 $n\le \omega$.
Object availability:
free access
Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
Prawa autorskie (c) 2024 Taras Banakh, Eliza Jabłońska
Date:
2024.03.03
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion;
Recenzowany artykuł
Language:
English
Source:
Topological Methods in Nonlinear Analysis; Vol 63, No 1 (March 2024); 197 - 208;
1230-3429
Publisher:
Nicolaus Copernicus University in Toruń
Relation: https://apcz.umk.pl/TMNA/article/view/49143/37868 ;https://apcz.umk.pl/TMNA/article/view/49143/37869
Subject:
Additive function;
mid-convex function;
continuity;
Haar-null set;
Haar-meager set;
null-finite set;
Haar-thin set;
Polish Abelian group;
Ger-Kuczma classes;
Primary: 28C10, 54C30, 54H05;
Secondary: 46A03
Identifier: https://apcz.umk.pl/TMNA/article/view/49143
Data provider:
Akademicka Platforma Czasopism

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