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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| Main Authors: | , |
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| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2021-10-01
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| Series: | Математичні Студії |
| Subjects: | |
| 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. |
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| ISSN: | 1027-4634 2411-0620 |