%0 Journal Article
%T Hyperconvexity and Tight Span Theory for Diversities
%A David Bryant
%A Paul F. Tupper
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.aim.2012.08.008
%X 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.
%U http://arxiv.org/abs/1006.1095v5