On pseudobounded and premeage paratopological groups

  • A.V. Ravsky Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
  • T.O. Banakh Ivan Franko National University of Lviv, Lviv, Ukraine
Keywords: topologized group; paratopological group


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.


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How to Cite
Ravsky A, Banakh T. On pseudobounded and premeage paratopological groups. Mat. Stud. [Internet]. 2021Oct.27 [cited 2022Jan.20];56(1):20-7. Available from: http://www.matstud.org.ua/ojs/index.php/matstud/article/view/261