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

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 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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Published
2021-10-27
How to Cite
Ravsky, A., & Banakh, T. (2021). On pseudobounded and premeage paratopological groups. Matematychni Studii, 56(1), 20-27. https://doi.org/10.30970/ms.56.1.20-27
Section
Articles