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arXiv · 2205.09718

Basic Metric Geometry of the Bottleneck Distance

Mauricio Che·Fernando Galaz-García·Luis Guijarro·Ingrid Membrillo Solis·Motiejus Valiunas
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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.

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Mauricio Che, Fernando Galaz-García, Luis Guijarro, Ingrid Membrillo Solis, Motiejus Valiunas. 2022-05-19. Basic Metric Geometry of the Bottleneck Distance. https://doi.org/10.1090/proc/16776

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