An isometric extensor of metrics
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917780062732288 |
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| author | Ishiki, Yoshito |
| author_facet | Ishiki, Yoshito |
| contents | In this paper, for a metrizable space $Z$, we consider the space of metrics that generate the same topology of $Z$, and that space of metrics is equipped with the supremum metrics. For a metrizable space $X$ and a closed subset $A$ of it, we construct a map $E$ from the space of metrics on $A$ into the space of metrics on $X$ such that $E$ is an extension of metrics and preserves the supremum metrics between metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An isometric extensor of metrics Ishiki, Yoshito Metric Geometry General Topology In this paper, for a metrizable space $Z$, we consider the space of metrics that generate the same topology of $Z$, and that space of metrics is equipped with the supremum metrics. For a metrizable space $X$ and a closed subset $A$ of it, we construct a map $E$ from the space of metrics on $A$ into the space of metrics on $X$ such that $E$ is an extension of metrics and preserves the supremum metrics between metrics. |
| title | An isometric extensor of metrics |
| topic | Metric Geometry General Topology |
| url | https://arxiv.org/abs/2407.03030 |