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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2021-10-01
|
| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/261 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850095274143252480 |
|---|---|
| author | A.V. Ravsky T.O. Banakh |
| author_facet | A.V. Ravsky T.O. Banakh |
| author_sort | A.V. Ravsky |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5799e9b33d11476a8210b8dacb2b3bd4 |
| institution | DOAJ |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2021-10-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-5799e9b33d11476a8210b8dacb2b3bd42025-08-20T02:41:29ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202021-10-01561202710.30970/ms.56.1.20-27261On pseudobounded and premeage paratopological groupsA.V. Ravsky0T.O. Banakh1Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of UkraineIvan Franko National University of Lviv, Lviv, UkraineLet $G$ 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.http://matstud.org.ua/ojs/index.php/matstud/article/view/261topologized group; paratopological group |
| spellingShingle | A.V. Ravsky T.O. Banakh On pseudobounded and premeage paratopological groups Математичні Студії topologized group; paratopological group |
| title | On pseudobounded and premeage paratopological groups |
| title_full | On pseudobounded and premeage paratopological groups |
| title_fullStr | On pseudobounded and premeage paratopological groups |
| title_full_unstemmed | On pseudobounded and premeage paratopological groups |
| title_short | On pseudobounded and premeage paratopological groups |
| title_sort | on pseudobounded and premeage paratopological groups |
| topic | topologized group; paratopological group |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/261 |
| work_keys_str_mv | AT avravsky onpseudoboundedandpremeageparatopologicalgroups AT tobanakh onpseudoboundedandpremeageparatopologicalgroups |