Geometry of Geometric Data Set I
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910069224898560 |
|---|---|
| author | Yokota, Shigeaki |
| author_facet | Yokota, Shigeaki |
| contents | Hanika, Schneider, and Stumme introduced geometric data set as a generalization of metric measure space for the computation of the observable diameter, and extended the observable distance between metric measure spaces to that between geometric data sets. In this paper, we begin by proving the non-separability of the observable distance between geometric data sets. We then extend the box distance between mm-spaces to that between geometric data sets and prove its completeness and non-separability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23316 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry of Geometric Data Set I Yokota, Shigeaki Metric Geometry 53C23 Hanika, Schneider, and Stumme introduced geometric data set as a generalization of metric measure space for the computation of the observable diameter, and extended the observable distance between metric measure spaces to that between geometric data sets. In this paper, we begin by proving the non-separability of the observable distance between geometric data sets. We then extend the box distance between mm-spaces to that between geometric data sets and prove its completeness and non-separability. |
| title | Geometry of Geometric Data Set I |
| topic | Metric Geometry 53C23 |
| url | https://arxiv.org/abs/2603.23316 |