Schur ultrafilters and Bohr compactifications of topological groups
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912298349625344 |
|---|---|
| author | Bardyla, Serhii Zlatoš, Pavol |
| author_facet | Bardyla, Serhii Zlatoš, Pavol |
| contents | In this paper we investigate Schur ultrafilters on groups. Using the algebraic structure of Stone-Čech compactifications of discrete groups and Schur ultrafilters, we give a new description of Bohr compactifications of topological groups. This approach allows us to characterize chart groups that are topological groups. Namely, a chart group $G$ is a topological group if and only if each Schur ultrafilter on $G$ converges to the unit of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schur ultrafilters and Bohr compactifications of topological groups Bardyla, Serhii Zlatoš, Pavol General Topology Group Theory Logic In this paper we investigate Schur ultrafilters on groups. Using the algebraic structure of Stone-Čech compactifications of discrete groups and Schur ultrafilters, we give a new description of Bohr compactifications of topological groups. This approach allows us to characterize chart groups that are topological groups. Namely, a chart group $G$ is a topological group if and only if each Schur ultrafilter on $G$ converges to the unit of $G$. |
| title | Schur ultrafilters and Bohr compactifications of topological groups |
| topic | General Topology Group Theory Logic |
| url | https://arxiv.org/abs/2409.07280 |