A factorization of metric spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912815205318656 |
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| author | Ishiki, Yoshito |
| author_facet | Ishiki, Yoshito |
| contents | We first prove that for every metrizable space $X$, for every closed subset $F$ whose complement is zero-dimensional, the space $X$ can be embedded into a product space of the closed subset $F$ and a metrizable zero-dimensional space as a closed subset. Using this theorem, we next show the existence of extensors of metrics and ultrametrics, which preserve properties of metrics such as the completeness, the properness, being an ultrametrics, its fractal dimensions, and large scale structures. This result contains some of the author's extension theorems of ultrametrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13409 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A factorization of metric spaces Ishiki, Yoshito General Topology Metric Geometry We first prove that for every metrizable space $X$, for every closed subset $F$ whose complement is zero-dimensional, the space $X$ can be embedded into a product space of the closed subset $F$ and a metrizable zero-dimensional space as a closed subset. Using this theorem, we next show the existence of extensors of metrics and ultrametrics, which preserve properties of metrics such as the completeness, the properness, being an ultrametrics, its fractal dimensions, and large scale structures. This result contains some of the author's extension theorems of ultrametrics. |
| title | A factorization of metric spaces |
| topic | General Topology Metric Geometry |
| url | https://arxiv.org/abs/2212.13409 |