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Peer-reviewedCC BYTopology and its Applications

An interpolation of metrics and spaces of metrics

  • Yoshito Ishiki1
  1. 1Department of Mathematical Sciences, Tokyo Metropolitan University, Minami-osawa Hachioji Tokyo 192-0397, Japan
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Abstract

As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli spaces of metrics. We observe that various sets of all metrics with properties appearing in metric geometry are dense intersections of countably many open subsets in spaces of metrics on metrizable spaces. For instance, our study is applicable to the set of all non-doubling metrics and the set of all non-uniformly disconnected metrics.

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Cite

BibTeXRIS
BibTeX
@article{ishiki2026interpolation,
  title = {{An interpolation of metrics and spaces of metrics}},
  author = {Yoshito Ishiki},
  journal = {Topology and its Applications},
  year = {2026},
  month = may,
  doi = {10.1016/j.topol.2026.109856},
  url = {https://doi.org/10.1016/j.topol.2026.109856},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - An interpolation of metrics and spaces of metrics
AU  - Yoshito Ishiki
PY  - 2026
DA  - 2026/05/14
JO  - Topology and its Applications
DO  - 10.1016/j.topol.2026.109856
UR  - https://doi.org/10.1016/j.topol.2026.109856
AB  - As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli spaces of metrics. We observe that various sets of all metrics with properties appearing in metric geometry are dense intersections of countably many open subsets in spaces of metrics on metrizable spaces. For instance, our study is applicable to the set of all non-doubling metrics and the set of all non-uniformly disconnected metrics.
SN  - 0166-8641
SN  - 1879-3207
ER  -