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Basic metric geometry of the bottleneck distance

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


Luis Guijarro

Ingrid Membrillo Solis

Motiejus Valiunas


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.


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,

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
Public URL
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