Hyperconvexity and tight-span theory for diversities

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Abstract

The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has applications to metric classification and data visualisation. Here we introduce a generalisation of metrics, called diversities, and demonstrate that the rich theory associated to metric tight spans and hyperconvexity extends to a seemingly richer theory of diversity tight spans and hyperconvexity. © 2012 Elsevier Ltd.

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Bryant, D., & Tupper, P. F. (2012). Hyperconvexity and tight-span theory for diversities. Advances in Mathematics, 231(6), 3172–3198. https://doi.org/10.1016/j.aim.2012.08.008

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