Related papers: Topological properties of Wazewski dendrite groups

We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure $M$, Polish group $G$ of permutations of $M$, and $n \geq 1$,…

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a…

This paper presents a discrete homotopy theory and a discrete homology theory for finite posets. In particular, the discrete and classical homotopy groups of finite posets are always isomorphic. Moreover, this discrete homology theory is…

For a non-compact n-manifold M let H(M) denote the group of homeomorphisms of M endowed with the Whitney topology and H_c(M) the subgroup of H(M) consisting of homeomorphisms with compact support. It is shown that the group H_c(M) is…

A topological gyrogroup is a gyrogroup endowed with a topology such that the binary operation is jointly continuous and the inverse mapping is also continuous. It is shown that each compact subset of a topological gyrogroup with an…

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…

Let $G$ be a locally compact Polish group. A metrizable $G$-flow $Y$ is called model-universal if by considering the various invariant probability measures on $Y$, we can recover every free action of $G$ on a standard Lebesgue space up to…

Given a locally compact Polish space X, a necessary and sufficient condition for a group G of homeomorphisms of X to be the full isometry group of (X,d) for some proper metric d on X is given. It is shown that every locally compact Polish…

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite…

We study minimal sets on continua $X$ with a dense free interval $J$ and a locally connected remainder. This class of continua includes important spaces such as the topologist's sine curve or the Warsaw circle. In the case when minimal sets…

The symmetrized bidisc \[ G \stackrel{\rm{def}}{=}\{(z+w,zw):|z|<1,\ |w|<1\} \] has interesting geometric properties. While it has a plentiful supply of complex geodesics and of automorphisms, there is nevertheless a unique complex geodesic…

A group $G$ has property $R_\infty$ if for every $\phi\in Aut(G)$, there are an infinite number of $\phi$-twisted conjugacy classes of elements in $G$. In this note, we determine the $R_\infty$-property for $G=\pi_1(M)$ for all geometric…

Each topological group $G$ admits a unique universal minimal dynamical system $(M(G),G)$. When $G$ is a non-compact locally compact group the phase space $M(G)$ of this universal system is non-metrizable. There are however topological…

We identify four countable topological spaces $S_2$, $S_1$, $S_D$, and $S_0$ which serve as canonical examples of topological spaces which fail to be quasi-Polish. These four spaces respectively correspond to the $T_2$, $T_1$, $T_D$, and…

We investigate the automorphism groups of $\aleph\_0$-categorical structures and prove that they are exactly the Roelcke precompact Polish groups. We show that the theory of a structure is stable if and only if every Roelcke uniformly…

In this paper we investigate the connections between Ramsey properties of Fraisse classes K and the universal minimal flow M(G_K) of the automorphism group G_K of their Fraisse limits. As an extension of a result of Kechris, Pestov and…

We give a complete characterization of the graph products of cyclic groups admitting a Polish group topology, and show that they are all realizable as the group of automorphisms of a countable structure. In particular, we characterize the…

Let $G$ be a non-compact semisimple Lie group with finite centre and finitely many components. We show that any finitely generated group $\Gamma$ which is quasi-isometric to an irreducible lattice in $G$ has the $R_\infty$-property, namely,…

Given a class C of subgroups of a topological group G, we say that a subgroup H in C is a universal C subgroup of G if every subgroup K in C is a continuous homomorphic preimage of H. Such subgroups may be regarded as complete members of C…

We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…