Metric duality for Abelian groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916522525458432 |
|---|---|
| author | Niemiec, Piotr |
| author_facet | Niemiec, Piotr |
| contents | The main aim of the paper is to introduce the concept of metric duality in the category of topological Abelian groups that extends the classical notion of duality for normed vector spaces and behaves quite nicely for LCA groups (equipped with nice metrics). In particular, it is shown that each Polish LCA group admits a reflexive proper metric and, more generally, all LCA groups possess reflexive (proper) metric structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metric duality for Abelian groups Niemiec, Piotr Group Theory Primary 22D35, Secondary 46B10, 43A40 The main aim of the paper is to introduce the concept of metric duality in the category of topological Abelian groups that extends the classical notion of duality for normed vector spaces and behaves quite nicely for LCA groups (equipped with nice metrics). In particular, it is shown that each Polish LCA group admits a reflexive proper metric and, more generally, all LCA groups possess reflexive (proper) metric structures. |
| title | Metric duality for Abelian groups |
| topic | Group Theory Primary 22D35, Secondary 46B10, 43A40 |
| url | https://arxiv.org/abs/2406.19924 |