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Basic Metric Geometry of the Bottleneck Distance
- Publication Year :
- 2022
-
Abstract
- Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the bottleneck distance. We investigate the basic metric properties of the spaces $\mathcal{D}_\infty(X,A)$ and obtain characterizations of their metrizability, completeness, separability, and geodesicity.<br />Comment: Final version. To appear in Proceedings of the AMS
- Subjects :
- Mathematics - Metric Geometry
Mathematics - Algebraic Topology
53C23, 55N31, 54F45
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2205.09718
- Document Type :
- Working Paper