Basic metric geometry of the bottleneck distance

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

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. (2024). Basic metric geometry of the bottleneck distance. Proceedings of the American Mathematical Society, 152(8), 3575-3591. https://doi.org/10.1090/proc/16776

• Journal Article Type: Article
• Acceptance Date: Jan 4, 2024
• Online Publication Date: Jun 12, 2024
• Publication Date: 2024-08
• Deposit Date: Jan 19, 2024
• Publicly Available Date: Jun 12, 2024
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 152
• Issue: 8
• Pages: 3575-3591
• DOI: https://doi.org/10.1090/proc/16776
• Public URL: https://durham-repository.worktribe.com/output/2150611