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Basic metric geometry of the bottleneck distance

Che, Mauricio; Galaz-García, Fernando; Guijarro, Luis; Membrillo Solis, Ingrid; Valiunas, Motiejus

Authors

Luis Guijarro

Ingrid Membrillo Solis

Motiejus Valiunas



Abstract

Given a metric pair (X, A), i.e. a metric space X and a distinguished closed set A ⊂ X, one may construct in a functorial way a pointed pseudometric space D∞(X, A) of persistence diagrams equipped with the bottleneck distance. We investigate the basic metric properties of the spaces D∞(X, A) and obtain characterizations of their metrizability, completeness, separability, and geodesicity.

Citation

Che, M., Galaz-García, F., Guijarro, L., Membrillo Solis, I., & Valiunas, M. (in press). Basic metric geometry of the bottleneck distance. Proceedings of the American Mathematical Society, https://doi.org/10.1090/proc/16776

Journal Article Type Article
Acceptance Date Jan 4, 2024
Deposit Date Jan 19, 2024
Journal Proceedings of the American Mathematical Society
Print ISSN 0002-9939
Electronic ISSN 1088-6826
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
DOI https://doi.org/10.1090/proc/16776
Public URL https://durham-repository.worktribe.com/output/2150611
Publisher URL https://www.ams.org/journals/proc/0000-000-00/?active=recent