A Universal Separable Diversity

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....

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Autores principales:	Bryant David, Nies André, Tupper Paul
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	diversities urysohn space katetov functions universality ultrahomogeneity 51f99 54e50 54e99 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/f8be5f5af176464ebff761d35c410a9d
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id	oai:doaj.org-article:f8be5f5af176464ebff761d35c410a9d
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spelling	oai:doaj.org-article:f8be5f5af176464ebff761d35c410a9d2021-12-05T14:10:38ZA Universal Separable Diversity2299-327410.1515/agms-2017-0008https://doaj.org/article/f8be5f5af176464ebff761d35c410a9d2017-12-01T00:00:00Zhttps://doi.org/10.1515/agms-2017-0008https://doaj.org/toc/2299-3274The 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.Bryant DavidNies AndréTupper PaulDe Gruyterarticlediversitiesurysohn spacekatetov functionsuniversalityultrahomogeneity51f9954e5054e99AnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 5, Iss 1, Pp 138-151 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	diversities urysohn space katetov functions universality ultrahomogeneity 51f99 54e50 54e99 Analysis QA299.6-433
spellingShingle	diversities urysohn space katetov functions universality ultrahomogeneity 51f99 54e50 54e99 Analysis QA299.6-433 Bryant David Nies André Tupper Paul A Universal Separable Diversity
description	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.
format	article
author	Bryant David Nies André Tupper Paul
author_facet	Bryant David Nies André Tupper Paul
author_sort	Bryant David
title	A Universal Separable Diversity
title_short	A Universal Separable Diversity
title_full	A Universal Separable Diversity
title_fullStr	A Universal Separable Diversity
title_full_unstemmed	A Universal Separable Diversity
title_sort	universal separable diversity
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/f8be5f5af176464ebff761d35c410a9d
work_keys_str_mv	AT bryantdavid auniversalseparablediversity AT niesandre auniversalseparablediversity AT tupperpaul auniversalseparablediversity AT bryantdavid universalseparablediversity AT niesandre universalseparablediversity AT tupperpaul universalseparablediversity
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A Universal Separable Diversity

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