Dimensions of ordered spaces and Lorentzian length spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916149346697216 |
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| author | Müller, Olaf |
| author_facet | Müller, Olaf |
| contents | After calculating the Dushnik-Miller dimension of Minkowski spaces to be countable infinity, we define a novel notion of dimension for ordered spaces recovering the correct manifold dimension and obtain a corresponding obstruction for the existence of injective monotonous maps between Lorentzian length spaces. Furthermore we induce metrics on Cauchy subsets, relate respective Hausdorff dimensions, prove existence of rushing Cauchy functions with a given Cauchy zero locus and consider collapse phenomena in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11237 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dimensions of ordered spaces and Lorentzian length spaces Müller, Olaf Metric Geometry After calculating the Dushnik-Miller dimension of Minkowski spaces to be countable infinity, we define a novel notion of dimension for ordered spaces recovering the correct manifold dimension and obtain a corresponding obstruction for the existence of injective monotonous maps between Lorentzian length spaces. Furthermore we induce metrics on Cauchy subsets, relate respective Hausdorff dimensions, prove existence of rushing Cauchy functions with a given Cauchy zero locus and consider collapse phenomena in this setting. |
| title | Dimensions of ordered spaces and Lorentzian length spaces |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2303.11237 |