# A Universal Separable Diversity

David Bryant; André Nies; Paul Tupper

Analysis and Geometry in Metric Spaces (2017)

- Volume: 5, Issue: 1, page 138-151
- ISSN: 2299-3274

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topDavid 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 -

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