Two-point dilation-homogeneous metric spaces
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929661564420096 |
|---|---|
| author | Niemiec, Piotr |
| author_facet | Niemiec, Piotr |
| contents | The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there exists a (bijective) dilation on X that fixes a and sends b to c. As a consequence, we obtain a new characterisation of the Euclidean spaces: these are (up to isometry) precisely all metric spaces that have the above two properties, and (in addition) contain three distinct points x, y, z that are metrically collinear (that is, for which d(x,z) = d(x,y)+d(y,z)). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-point dilation-homogeneous metric spaces Niemiec, Piotr Metric Geometry Primary 22F30, Secondary 51F99, 57S99 The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there exists a (bijective) dilation on X that fixes a and sends b to c. As a consequence, we obtain a new characterisation of the Euclidean spaces: these are (up to isometry) precisely all metric spaces that have the above two properties, and (in addition) contain three distinct points x, y, z that are metrically collinear (that is, for which d(x,z) = d(x,y)+d(y,z)). |
| title | Two-point dilation-homogeneous metric spaces |
| topic | Metric Geometry Primary 22F30, Secondary 51F99, 57S99 |
| url | https://arxiv.org/abs/2501.03382 |