Related papers: On metrizable enveloping semigroups

We show that every group $H$ of at most exponential growth with respect to some left invariant metric admits a bi-Lipschitz embedding into a finitely generated group $G$ such that $G$ is amenable (respectively, solvable, satisfies a…

We provide a necessary and sufficient condition for the embeddability of a metrizable group into semigroup compactifications associated to uniformly continuous functions. Our result employs a technique used by I. Ben Yaacov, A. Berenstein…

A topological space $X$ is called strongly $\sigma$-metrizable if $X=\bigcup_{n\in\omega}X_n$ for an increasing sequence $(X_n)_{n\in\omega}$ of closed metrizable subspaces such that every convergence sequence in $X$ is contained in some…

Let $G$ be a non-amenable countable group. We show that every almost automorphic $G$-action on a compact Hausdorff space, with a maximal equicontinuous factor whose phase space is a Cantor set, admits invariant probability measures (this…

We study isometric $G$-spaces and the question of when their maximal equivariant compactification is the Gromov compactification (meaning that it coincides with the compactification generated by the distance functions to points). Answering…

In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of…

We have shown recently that, given a metric space $X$, the coarse equivalence classes of metrics on the two copies of $X$ form an inverse semigroup $M(X)$. Here we study the property of idempotents in $M(X)$ of being finite or infinite,…

It is known that for every second countable locally compact group G, there exists a proper G-invariant metric which induces the topology of the group. This is no longer true for coset spaces G/H viewed as G-spaces. We study necessary and…

By proving that, if the quotient space S(X) of the connected components of the locally compact metric space (X,d) is compact, then the full group I(X,d) of isometries of X is closed in C(X,X) with respect to the pointwise topology, i.e.,…

Symbolic Extension Entropy Theorem (SEET) describes the possibility of a lossless digitalization of a dynamical system by extending it to a subshift. It gives an estimate on the entropy of symbolic extensions (and the necessary number of…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called (1) $\mathcal C$-$closed$ if $X$ is closed in every topological semigroup $Y\in\mathcal C$ containing $X$ as a discrete subsemigroup, (2) $ideally$ $\mathcal…

Let $(X,\rho,G)$ be a $G-$action topological system, where $G$ is a countable infinite discrete amenable group and $X$ a compact metric space. We prove a variational principle for topological entropy of saturated sets for systems which have…

We present several known and new results on the Baire category properties in topological groups. In particular, we prove that a Baire topological group $X$ is metrizable if and only if $X$ is point-cosmic if and only if $X$ is a…

Let $G$ be a right-angled Artin group with $|\mathrm{Out}(G)|<+\infty$. We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$, with an $L^1$-integrable measure equivalence cocycle towards $G$, then $H$ is…

Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as a counterpart of Bowen topological entropy. In the present paper, we will give a systematically study to the packing topological entropy for…

We establish some geometrical properties of the space of idempotent probability measures. In particular, for a compact $X$ it is established that if the space $I_{3}(X)\backslash X$ is hereditary normally, then $X$ is metrizable; some…

The notion of a proper Ellis semigroup compactification is introduced. Ellis's functional approach shows how to obtain them from totally bounded equiuniformities on a phase space $X$ when the acting group $G$ is with the topology of…

In this paper, it is shown that every right $\omega$-narrow strongly topological gyrogroup $G$ is right $\omega$-balanced by applying the gyrosemidirect product groups. Then we investigate the class of $\sigma$-compact strongly topological…

We say that a finite metric space $X$ can be embedded almost isometrically into a class of metric spaces $C$, if for every $\epsilon > 0$ there exists an embedding of $X$ into one of the elements of $C$ with the bi-Lipschitz distortion less…

An action of a topological semigroup S on X is compactifiable if this action is a restriction of a jointly continuous action of S on a Hausdorff compact space Y. A topological semigroup S is compactifiable if the left action of S on itself…