  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.
