{"title":"A Borel linear subspace of R^\\omega that cannot be covered by countably many closed Haar-meager sets","authors":"Taras Banakh, Eliza Jabłońska","doi":"10.12775/tmna.2023.002","DOIUrl":null,"url":null,"abstract":"We prove that the countable product of lines contains a Haar-null Haar-meager \nBorel linear subspace $L$\nthat cannot be covered by countably many closed Haar-meager sets.\nThis example is applied to studying the interplay between various classes of ``large''\nsets and Kuczma-Ger classes in the topological vector spaces ${\\mathbb R}^n$ for $n\\le \\omega$.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topological Methods in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12775/tmna.2023.002","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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 $n\le \omega$.
期刊介绍:
Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.