A Universal Separable Diversity

David Bryant, André Nies, and Paul Tupper. "A Universal Separable Diversity." Analysis and Geometry in Metric Spaces 5.1 (2017): 138-151. <http://eudml.org/doc/288401>.

@article{DavidBryant2017,
abstract = {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.},
author = {David Bryant, André Nies, Paul Tupper},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Diversities; Urysohn space; Katetov functions; universality; ultrahomogeneity},
language = {eng},
number = {1},
pages = {138-151},
title = {A Universal Separable Diversity},
url = {http://eudml.org/doc/288401},
volume = {5},
year = {2017},
}

TY - JOUR
AU - David Bryant
AU - André Nies
AU - Paul Tupper
TI - A Universal Separable Diversity
JO - Analysis and Geometry in Metric Spaces
PY - 2017
VL - 5
IS - 1
SP - 138
EP - 151
AB - 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.
LA - eng
KW - Diversities; Urysohn space; Katetov functions; universality; ultrahomogeneity
UR - http://eudml.org/doc/288401
ER -