Related papers: Absolute Continuity and Large-Scale Geometry of Po…

We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of…

Given an irreducible non-spherical non-affine (possibly non-proper) building $X$, we give sufficient conditions for a group $G < \Aut(X)$ to admit an infinite-dimensional space of non-trivial quasi-morphisms. The result applies to all…

We study permanence results for almost quasi-isometries, the maps arising from the Gromov construction of finitely generated random groups that contain expanders (and hence that are not C*-exact). We show that the image of a sequence of…

We prove an almost continuous version of Dye's theorem: any two non-atomic probability measure preserving homeomorphisms of Polish spaces are almost continuously orbit equivalent. More precisely they are orbit equivalent by a map which is…

In this paper we extend a previous result of the author [Lis07] of characterization of absolutely continuous curves in Wasserstein spaces to a more general class of spaces: the spaces of probability measures endowed with the…

Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these…

Let $G$ and $H$ be locally compact groups and consider their associate spaces of almost periodic functions $AP(G)$ and $AP(H)$. We investigate the continuous group homomorphisms induced by isometries of $AP(G)$ into $AP(H)$. Among others,…

Sorin Popa initiated the study of Polish groups which are embeddable into the unitary group of a separable finite von Neumann algebra. Such groups are called of finite type. We give necessary and sufficient conditions for Polish groups to…

The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual…

We study full groups of minimal actions of countable groups by homeomorphisms on a Cantor space $X$, showing that these groups do not admit a compatible Polish group topology and, in the case of $\Z$-actions, are coanalytic non-Borel inside…

A class of almost paratopological groups is introduced, which (1) contains paratopological groups and Hausdorff quasitopological groups; (2) is closed under products; (3) subgroups. Almost paratopological $T_1$ groups $G$ are characterized…

We study notions of persistent homotopy groups of compact metric spaces together with their stability properties in the Gromov-Hausdorff sense. We pay particular attention to the case of fundamental groups, for which we obtain a more…

Let $\Gamma(X)$ be the inverse semigroup of partial homeomorphisms between open subsets of a compact metric space $X$. There is a topology, denoted $\tau_{hco}$, that makes $\Gamma(X)$ a topological inverse semigroup. We address the…

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…

In this paper we explore the extent to which the algebraic structure of a monoid $M$ determines the topologies on $M$ that are compatible with its multiplication. Specifically we study the notions of automatic continuity; minimal Hausdorff…

This paper presents a study of generic elements in full isometry groups of Polish ultrametric spaces. We obtain a complete characterization of Polish ultrametric spaces X whose isometry group Iso(X) contains an open subgroup H with ample…

The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group…

Let $G$ be a topological group and let $\mu$ be the Lebesgue measure on the interval $[0,1]$. We let $L_0(G)$ to be the topological group of all $\mu$-equivalence classes of $\mu$-measurable functions defined on [0,1] with values in $G$,…

Let $\Aut(G)$ denote the group of (bi-)continuous automorphisms %and $\Out(G)$ the outer automorphism group of a non-Archimedean Polish group~$G$. We show that for any such $G$ with an invariant countable basis of open subgroups, the group…

It is well-known that Polish Roelcke precompact groups are the groups that can be represented as automorphism groups of $\aleph_0$-categorical structures in continuous logic and that there is a precise correspondence between properties of…