Extension of mappings on metric spaces
J. de Groot, R. McDowell (1960)
Fundamenta Mathematicae
Similarity:
Displaying similar documents to “On the group of isometries of the Urysohn universal metric space”
Extension of mappings on metric spaces
On the thickness of topological spaces
Bernard Brunet (1995)
Annales mathématiques Blaise Pascal
Similarity:
Closed, continuous images of complete metric spaces
K. Van Doren (1973)
Fundamenta Mathematicae
Similarity:
Metric spaces in which Prohorov's theorem is not valid
Preiss, D.
Similarity:
A Universal Separable Diversity
David Bryant, André Nies, Paul Tupper (2017)
Analysis and Geometry in Metric Spaces
Similarity:
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...
Non-archimedian metrizability of topological groups
G. Rangan (1970)
Fundamenta Mathematicae
Similarity:
Topology of the isometry group of the Urysohn space
Julien Melleray (2010)
Fundamenta Mathematicae
Similarity:
Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space ℓ²(ℕ). The proof is based on a lemma about extensions of metric spaces by finite metric spaces, which we also use to investigate (answering a question of I. Goldbring) the relationship, when A,B are finite subsets of the Urysohn space, between the group of isometries fixing A pointwise,...