47 citations · 181 across the 30 of their papers we have counts for
7 papers · 1 filter
On Dual surjunctivity and applications
Michal Doucha, Jakub Gismatullin
We explore the dual version of Gottschalk's conjecture recently introduced by Capobianco, Kari, and Taati, and the notion of dual surjunctivity in general. We show that dual surjun…
Property (T), finite-dimensional representations, and generic representations
Michal Doucha, Maciej Malicki, Alain Valette
Let be a discrete group with property (T). It is a standard fact that, in a unitary representation of on a Hilbert space , almost invariant vectors are close t…
Generic representations of countable groups
Michal Doucha, Maciej Malicki
The paper is devoted to a study of generic representations (homomorphisms) of discrete countable groups in Polish groups , i.e. those elements in the Polish space $\mathrm{R…
Universal actions and representations of locally finite groups on metric spaces
Michal Doucha
We construct a universal action of a countable locally finite group (the Hall's group) on a separable metric space by isometries. This single action contains all actions of all cou…
Embeddings into monothetic groups
Michal Doucha
We provide a very short elementary proof that every bounded separable metric group embeds into a monothetic bounded metric group, in such a way that the result of Morris and Pestov…
Metric topological groups: their metric approximation and metric ultraproducts
Michal Doucha
We define a metric ultraproduct of topological groups with left-invariant metric, and show that there is a countable sequence of finite groups with left-invariant metric whose metr…