A Universal Separable Diversity

• Autorzy: David Bryant , André Nies , Paul Tupper
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Diversities; Urysohn space; Katetov functions; universality; ultrahomogeneity

Kategorie tematyczne

• 51F99: None of the above, but in this section
• 54E99: None of the above, but in this section
• 54E50: Complete metric spaces

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 138-151

Daty

wydano

2017-12-20

otrzymano

2017-09-06

zaakceptowano

2017-11-10

online

2017-12-29

Twórcy

autor

David Bryant

• ---

autor

André Nies

• ,

autor

Paul Tupper

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Identyfikatory

DOI

10.1515/agms-2017-0008