Displaying similar documents to “Topology of the isometry group of the Urysohn space”

A Universal Separable Diversity

David Bryant, André Nies, Paul Tupper (2017)

Analysis and Geometry in Metric Spaces

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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...

On metric σ-discrete spaces

Szymon Plewik, Marta Walczyńska (2016)

Banach Center Publications

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By studying dimensional types of metric scattered spaces, we consider the wider class of metric σ-discrete spaces. Applying techniques relevant to this wider class, we present new proofs of some embeddable properties of countable metric spaces in such a way that they can be generalized onto uncountable metric scattered spaces. Related topics are also explored, which gives a few new results.