{"title":"On pseudobounded and premeage paratopological groups","authors":"A. Ravsky, T. Banakh","doi":"10.30970/ms.56.1.20-27","DOIUrl":null,"url":null,"abstract":"Let $G$ be a paratopological group.Following F.~Lin and S.~Lin, we say that the group $G$ is pseudobounded,if for any neighborhood $U$ of the identity of $G$,there exists a natural number $n$ such that $U^n=G$.The group $G$ is $\\omega$-pseudobounded,if for any neighborhood $U$ of the identity of $G$, the group $G$ is aunion of sets $U^n$, where $n$ is a natural number.The group $G$ is premeager, if $G\\ne N^n$ for any nowhere dense subset $N$ of$G$ and any positive integer $n$.In this paper we investigate relations between the above classes of groups andanswer some questions posed by F. Lin, S. Lin, and S\\'anchez.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematychni Studii","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30970/ms.56.1.20-27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Let $G$ be a paratopological group.Following F.~Lin and S.~Lin, we say that the group $G$ is pseudobounded,if for any neighborhood $U$ of the identity of $G$,there exists a natural number $n$ such that $U^n=G$.The group $G$ is $\omega$-pseudobounded,if for any neighborhood $U$ of the identity of $G$, the group $G$ is aunion of sets $U^n$, where $n$ is a natural number.The group $G$ is premeager, if $G\ne N^n$ for any nowhere dense subset $N$ of$G$ and any positive integer $n$.In this paper we investigate relations between the above classes of groups andanswer some questions posed by F. Lin, S. Lin, and S\'anchez.