Related papers: Compactification de Chabauty des espaces sym\'etri…

For a connected Lie group $G$ and an automorphism $T$ of $G$, we consider the action of $T$ on Sub$_G$, the compact space of closed subgroups of $G$ endowed with the Chabauty topology. We study the action of $T$ on Sub$^p_G$, the closure in…

This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…

Let $G$ be a group and $\sigma, \tau$ be topological group topologies on $G$. We say that $\sigma$ is a successor of $\tau$ if $\sigma$ is strictly finer than $\tau$ and there is not a group topology properly between them. In this note, we…

We prove that if $T: X \to X$ is a selfmap of a set $X$ such that $\bigcap \{T^{n}X: n\in N}\}$ is a one-point set, then the set $X$ can be endowed with a compact Hausdorff topology so that $T$ is continuous.

H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite…

In this paper, we establish the compactification of the moduli space in symplectization and and studied the hidden symmetries of its boundary.

A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie…

The \emph{Bohr compactification} of an arbitrary topological group $G$ is defined as the group compactification $(bG,b)$ with the following universal property: for every continuous homomorphism $h$ from $G$ into a compact group $K$ there is…

We study Chabauty limits of the fixed-point group of $k$-points $H_k$ associated with an involutive $k$-automorphism $\theta$ of a connected linear reductive group $G$ defined over a non-Archimedean local field $k$ of characteristic zero.…

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…

In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$. The key to this approach is that in each case $G/P$ is the homogeneous model for a parabolic…

Let $X$ be a Hausdorff topological group and $G$ a locally compact subgroup of $X$. We show that $X$ admits a locally finite $\sigma$-discrete $G$-functionally open cover each member of which is $G$-homeomorphic to a twisted product…

We describe the order type of range sets of compact ultrametrics and show that an ultrametrizable infinite topological space $(X, \tau)$ is compact iff the range sets are order isomorphic for any two ultrametrics compatible with the…

We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, as compactness and strong compactness. In contrast with some…

Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…

The spectrum of an admissible subalgebra $\mathscr{A}(G)$ of $\mathscr{LUC}(G)$, the algebra of right uniformly continuous functions on a locally compact group $G$, constitutes a semigroup compactification $G^\mathscr{A}$ of $G$. In this…

Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic…

Let $G$ be a connected Lie group and $\text{Sub}_G$ be the space of closed subgroups of $G$ equipped with the Chabauty topology. In this article, we investigate the existence of invariant random subgroups of $G$ supported on various orbits…

In this paper we describe the local limits under conjugation of all closed connected subgroups of $SL_3(\mathbb{R})$ in the Chabauty topology.

Let $X$ be a locally compact topological space, $(Y,d)$ be a boundedly compact metric space and $LB(X,Y)$ be the space of all locally bounded functions from $X$ to $Y$. We characterize compact sets in $LB(X,Y)$ equipped with the topology of…