47 citations · 181 across the 30 of their papers we have counts for
6 papers · 1 filter
Lipschitz-free spaces over ultrametric spaces
Marek Cuth, Michal Doucha
We prove that the Lipschitz-free space over a separable ultrametric space has a monotone Schauder basis and is isomorphic to . This extends results of A. Dalet using an alt…
Metrical universality for groups
Michal Doucha
We prove that for any constant there exists a separable group equipped with a complete bi-invariant metric bounded by , isometric to the Urysohn sphere of diameter , th…
Metric Scott analysis
Itai Ben Yaacov, Michal Doucha, Andre Nies +1
We develop an analogue of the classical Scott analysis for metric structures and infinitary continuous logic. Among our results are the existence of Scott sentences for metric stru…
Non-universality of automorphism groups of uncountable ultrahomogeneous structures
Michal Doucha
In \cite{MbPe}, Mbombo and Pestov prove that the group of isometries of the generalized Urysohn space of density , for uncountable such that , is not a universal t…
Non-abelian group structure on the Urysohn space
Michal Doucha
Following the continuing interest in the Urysohn space and, more specifically, the recent problem area of finding and comparing group structures on the Urysohn space we prove that…
Scott rank of Polish metric spaces
Michal Doucha
Following the work of Friedman, Koerwien, Nies and Schlicht we positively answer their question whether the Scott rank of Polish metric spaces is countable.