Möbius structures, quasi-metrics, and completeness
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arXiv
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866911964234514432 |
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| author | Incerti-Medici, Merlin |
| author_facet | Incerti-Medici, Merlin |
| contents | We study cross ratios from an axiomatic viewpoint, also known as the study of Möbius spaces. We characterise cross ratios induced by quasi-metrics in terms of topological properties of their image. Furthermore, we generalise the notions of Cauchy-sequences and completeness to Möbius spaces and prove the existence of a unique completion under an extra assumption that, again, can be expressed in terms of the image of the cross ratio. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_10166 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Möbius structures, quasi-metrics, and completeness Incerti-Medici, Merlin Metric Geometry 51XX, 51Fxx, 51Hxx We study cross ratios from an axiomatic viewpoint, also known as the study of Möbius spaces. We characterise cross ratios induced by quasi-metrics in terms of topological properties of their image. Furthermore, we generalise the notions of Cauchy-sequences and completeness to Möbius spaces and prove the existence of a unique completion under an extra assumption that, again, can be expressed in terms of the image of the cross ratio. |
| title | Möbius structures, quasi-metrics, and completeness |
| topic | Metric Geometry 51XX, 51Fxx, 51Hxx |
| url | https://arxiv.org/abs/1706.10166 |