An interpolation of metrics and spaces of metrics
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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Geometric Analysis and Curvature Flows
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Topology and its Applications
- Publisher
- Elsevier BV
- Volume
- 388
- Pages
- 109856–109856
- Publication date
- 14 May 2026
- Language
- EN