Related papers: Locally precompact groups: (Local) realcompactness…
We describe the global structure of totally disconnected locally compact groups having a linear open compact subgroup. Among the applications, we show that if a non-discrete, compactly generated, topologically simple, totally disconnected…
For a locally quasi-convex (lqc) abelian group $G$, we give the first description of all compatible group topologies on $G$ and apply this result to the Mackey group problem for lqc groups. We characterize lqc abelian groups which are…
A topological group is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the group with its right uniformity is contained in an ambit. For n=0,1,2,..., every locally aleph_n bounded topological…
It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the…
We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…
A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…
It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are…
We study the locally compact abelian groups in the class $\mathfrak E_{<\infty}$, that is, having only continuous endomorphisms of finite topological entropy, and in its subclass $\mathfrak E_0$, that is, having all continuous endomorphisms…
If G is a locally essential subgroup of a compact abelian group K, then: (i) t(G)=w(G)=w(K), where t(G) is the tightness of G; (ii) if G is radial, then K must be metrizable; (iii) G contains a super-sequence S converging to 0 such that…
A compact manifold $M$ together with a Riemannian metric $h$ on its universal cover $\tilde M$ for which $\pi_1(M)$ acts by similarities is called a similarity structure. In the case where $\pi_1(M) \not\subset \mathrm{Isom}(\tilde M, h)$…
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…
In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in…
A topological group $(G,\mu)$ from a class $\mathcal G$ of MAP topological abelian groups will be called a {\it Mackey group} in $\mathcal G$ if it has the following property: if $\nu$ is a group topology in $G$ such that $(G,\nu)\in…
A group is small if it has countably many complete $n$-types over the empty set for each natural number n. More generally, a group $G$ is weakly small if it has countably many complete 1-types over every finite subset of G. We show here…
v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition…
We prove that each closed locally continuum- connected subspace of a finite dimensional topological group is locally compact. This allows us to construct many 1-dimensional metrizable separable spaces that are not homeomorphic to closed…
This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated…
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…
We study when a piecewise full group (a.k.a. topological full group) of homeomorphisms of the Cantor space $X$ can be given a non-discrete totally disconnected locally compact (t.d.l.c.) topology and give a criterion for the alternating…
In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising…