Discrete subgroups of normed spaces are free
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913459802734592 |
|---|---|
| author | Kania, Tomasz Kostana, Ziemowit |
| author_facet | Kania, Tomasz Kostana, Ziemowit |
| contents | Ancel, Dobrowolski, and Grabowski (Studia Math., 1994) proved that every countable discrete subgroup of the additive group of a normed space is free Abelian, hence isomorphic to the direct sum of a certain number of copies of the additive group of the integers. In the present paper, we take a set-theoretic approach based on the theory of elementary submodels and the Singular Compactness Theorem to remove the cardinality constraint from their result and prove that indeed every discrete subgroup of the additive group of a normed space is free Abelian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete subgroups of normed spaces are free Kania, Tomasz Kostana, Ziemowit Functional Analysis Group Theory Logic 46B20, 20K27 (primary), 46B26, 20K99 (secondary) Ancel, Dobrowolski, and Grabowski (Studia Math., 1994) proved that every countable discrete subgroup of the additive group of a normed space is free Abelian, hence isomorphic to the direct sum of a certain number of copies of the additive group of the integers. In the present paper, we take a set-theoretic approach based on the theory of elementary submodels and the Singular Compactness Theorem to remove the cardinality constraint from their result and prove that indeed every discrete subgroup of the additive group of a normed space is free Abelian. |
| title | Discrete subgroups of normed spaces are free |
| topic | Functional Analysis Group Theory Logic 46B20, 20K27 (primary), 46B26, 20K99 (secondary) |
| url | https://arxiv.org/abs/2408.03226 |