Topology of the isometry group of the Urysohn space

• Autorzy: Julien Melleray
• Języki publikacji: EN

Abstrakty

EN

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, the group of isometries fixing B pointwise, and the group of isometries fixing A ∩ B pointwise.

Kategorie tematyczne

• 22F99: None of the above, but in this section
• 51F99: None of the above, but in this section
• 54H11: Topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 207
• Numer: 3
• Strony: 273-287

Daty

wydano

2010

Twórcy

autor

Julien Melleray

• Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne Cedex, France

Identyfikatory

DOI

10.4064/fm207-3-4