Diversity_(mathematics)
Diversity (mathematics)
Generalization of metric spaces
In mathematics, a diversity is a generalization of the concept of metric space. The concept was introduced in 2012 by Bryant and Tupper,[1] who call diversities "a form of multi-way metric".[2] The concept finds application in nonlinear analysis.[3]
This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
|
Given a set , let be the set of finite subsets of . A diversity is a pair consisting of a set and a function satisfying
(D1) , with if and only if
and
(D2) if then .
Bryant and Tupper observe that these axioms imply monotonicity; that is, if , then . They state that the term "diversity" comes from the appearance of a special case of their definition in work on phylogenetic and ecological diversities. They give the following examples: