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Gluing Hyperconvex Metric Spaces

100%

Miesch B.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing along externally hyperconvex subsets leads to hyperconvex spaces. Furthermore, we show by an example that these two cases where gluing works are opposed and cannot be combined.

A Universal Separable Diversity

61%

Bryant D., Nies A., Tupper P.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

138-151

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.

Ograniczanie wyników

2 Analysis and Geometry in Metric Spaces

1 Bryant D.

1 Miesch B.

1 Nies A.

1 Tupper P.

1 2017

1 2015

Wyniki wyszukiwania

Gluing Hyperconvex Metric Spaces

A Universal Separable Diversity