An isometric extensor of metrics
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.03030
- arXiv:
- arXiv:2407.03030
- Bibcode:
- 2024arXiv240703030I
- Keywords:
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- Mathematics - Metric Geometry;
- Mathematics - General Topology
- E-Print:
- 36 pages. I have fixed gaps on topologies of Wasserstein spaces on arbitrary metric spaces. I have also provided a general observation on topologies on spaces of measurable functions using Lusin's theorem