Details

Autor(en) / Beteiligte

• Bryant, David
• Nies, André
• Tupper, Paul

Titel

A Universal Separable Diversity

Ist Teil von

• Analysis and Geometry in Metric Spaces, 2017-12, Vol.5 (1), p.138-151

Ort / Verlag

Berlin: De Gruyter Open

Erscheinungsjahr

2017

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• The Urysohn space is a separable complete metric space with two fundamental properties: (a) universality: every separable metric space can be isometrically embedded in it; (b) ultrahomogeneity: every finite isometry between two finite subspaces can be extended to an auto-isometry of the whole space. The Urysohn space is uniquely determined up to isometry within separable metric spaces by these two properties. We introduce an analogue of the Urysohn space for diversities, a recently developed variant of the concept of a metric space. In a diversity any finite set of points is assigned a non-negative value, extending the notion of a metric which only applies to unordered pairs of points.We construct the unique separable complete diversity that it is ultrahomogeneous and universal with respect to separable diversities.