Some isometry groups of Urysohn space
نویسنده
چکیده
We construct various isometry groups of Urysohn space (the unique complete separable metric space that is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.
منابع مشابه
1 1 Ju l 2 00 4 Some isometry groups of Urysohn space
We construct various isometry groups of Urysohn space (the unique complete separable metric space which is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.
متن کاملExtending Partial Isometries
We show that a finite metric space A admits an extension to a finite metric space B so that each partial isometry of A extends to an isometry of B. We also prove a more precise result on extending a single partial isometry of a finite metric space. Both these results have consequences for the structure of the isometry groups of the rational Urysohn metric space and the Urysohn metric space.
متن کاملOn the isometry group of the Urysohn space
We give a general criterion for the (bounded) simplicity of the automorphism groups of certain countable structures and apply it to show that the isometry group of the Urysohn space modulo the normal subgroup of bounded isometries is a simple group.
متن کاملRamsey Degrees of Finite Ultrametric Spaces, Ultrametric Urysohn Spaces and Dynamics of Their Isometry Groups
We study Ramsey-theoretic properties of several natural classes of finite ultrametric spaces, describe the corresponding Urysohn spaces and compute a dynamical invariant attached to their isometry groups.
متن کاملThe Generic Isometry and Measure Preserving Homeomorphism Are Conjugate to Their Powers
It is known that there is a comeagre set of mutually conjugate measure preserving homeomorphisms of Cantor space equipped with the coinflipping probability measure, i.e., Haar measure. We show that the generic measure preserving homeomorphism is moreover conjugate to all of its powers. It follows that the generic measure preserving homeomorphism extends to an action of (Q,+) by measure preservi...
متن کامل