Plastic metric spaces and groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917179609317376 |
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| author | Banakh, Taras Mazurenko, Oles Zavarzina, Olesia |
| author_facet | Banakh, Taras Mazurenko, Oles Zavarzina, Olesia |
| contents | A metric space is plastic if all its non-expansive bijections are isometries. We prove three main results: (1) every countable dense subspace of a normed space is not plastic, (2) every $k$-crowded separable metric space contains a plastic dense subspace, and (3) every strictly convex separable metric group contains a plastic dense subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Plastic metric spaces and groups Banakh, Taras Mazurenko, Oles Zavarzina, Olesia General Topology Functional Analysis Group Theory 03E50, 20K27, 46B04, 54E40 A metric space is plastic if all its non-expansive bijections are isometries. We prove three main results: (1) every countable dense subspace of a normed space is not plastic, (2) every $k$-crowded separable metric space contains a plastic dense subspace, and (3) every strictly convex separable metric group contains a plastic dense subgroup. |
| title | Plastic metric spaces and groups |
| topic | General Topology Functional Analysis Group Theory 03E50, 20K27, 46B04, 54E40 |
| url | https://arxiv.org/abs/2510.10537 |