On pseudobounded and premeage paratopological groups

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 o...

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Bibliographic Details
Main Authors: A.V. Ravsky, T.O. Banakh
Format: Article
Language:deu
Published: Ivan Franko National University of Lviv 2021-10-01
Series:Математичні Студії
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Online Access:http://matstud.org.ua/ojs/index.php/matstud/article/view/261
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Summary: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 a union 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 and answer some questions posed by F. Lin, S. Lin, and S\'anchez.
ISSN:1027-4634
2411-0620