Related papers: Thick Difference Sets of Haar Null Compact Sets in…

Suppose G is a topological group containing a (closed) topological copy of the Frechet-Urysohn fan. If G is a perfectly normal sequential space (a normal k-space) then every closed metrizable subset in $G$ is locally compact. Applying this…

We show that every non-Haar-null analytic subset of $\mathbb{Z}^\omega$ contains a non-Haar-null closed subset. Moreover, we also prove that the codes of Haar-null analytic subsets, and, consequently, closed Haar-null sets in the Effros…

Let X be compact abelian group and G its dual (a discrete group). If B is an infinite subset of G, let C_B be the set of all x in X such that <phi(x) : phi \in B> converges to 1. If F is a free filter on G, let D_F be the union of all the…

Certain topological properties of the group $\J(\k)$ of all formal one-variable power series with coefficients in a topological unitary ring $\k$ are considered. We show, in particular, that in the case when $\k=\Q$ the group $\J(\Q)$ has…

We show that every abstract homomorphism $\varphi$ from a locally compact group $L$ to a graph product $G_\Gamma$, endowed with the discrete topology, is either continuous or $\varphi(L)$ lies in a 'small' parabolic subgroup. In particular,…

We construct certain non-degenerate maps and sets, mainly in the complex-analytic category. For example, we show that for every countable subset S in an irreducible complex space X there exists a holomorphic map from the unit disk to X such…

For a separable locally compact but not compact metrizable space $X$, let $\alpha X = X \cup \{x_\infty\}$ be the one-point compactification with the point at infinity $x_\infty$. We denote by $EM(X)$ the space consisting of admissible…

We give a probabilistic proof of the Weyl integration formula on U(n), the unitary group with dimension $n$. This relies on a suitable definition of Haar measures conditioned to the existence of a stable subspace with any given dimension…

We construct holomorphic maps with a Siegel disk whose boundary is not locally connected (and is an indecomposable continuum), yet compactly contained in the domain of definition of the map. Our examples are injective and defined on a…

Let $G$ be an abelian Polish group, e.g. a separable Banach space. A subset $X \subset G$ is called Haar null (in the sense of Christensen) if there exists a Borel set $B \supset X$ and a Borel probability measure $\mu$ on $G$ such that…

Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.

In $\mathbb{R}^d$, a closed, convex set has zero Lebesgue measure if and only its interior is empty. More generally, in separable, reflexive Banach spaces, closed and convex sets are Haar null if and only if their interior is empty. We…

We construct a sequence of simple non-discrete totally disconnected locally compact (tdlc) groups separated by finiteness properties; that is, for every positive integer $n$ there exists a simple non-discrete tdlc group that is of type…

Let $G$ and $H$ be locally compact groups with fixed two-side-invariant Haar measures. A polyhomomorphism $G\to H$ is a closed subgroup $R\subset G\times H$ with a fixed Haar measure, whose marginals on $G$ and $H$ are dominated by the Haar…

For G = SL(3,R) and G = SO(2,n), we give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G has the property that there exists a compact subset C of G with CHC = G. To do this, we fix a Cartan…

It is known that exactness for a discrete group is equivalent to C*-exactness, i.e., the exactness of its reduced C*-algebra. The problem of whether this equivalence holds for general locally compact groups has recently been reduced by Cave…

Suppose $G$ is a connected noncompact locally compact group, $A,B$ are nonempty and compact subsets of $G$, $\mu$ is a left Haar measure on $G$. Assuming that $G$ is unimodular, and $ \mu(A^2) < K \mu(A) $ with $K>1$ a fixed constant, our…

For any topological group $G$ the dual object $\hat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat G$ is discrete, and we investigate…

We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to…

We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of…