Related papers: On the Hyperbolizing metric spaces

In \cite[\, An, V.T., Tuyen, Q.L. and Dung, V.N., Stone-type theorem on $b$-metric spaces and applications, Topology Appl. 185-186 (2015), 50-64.]{an}, An et al. had provided a sufficient condition for $b$-metric spaces to be metrizable.…

The Urysohn universal metric space U is characterized up to isometry by the following properties: (1) U is complete and separable; (2) U contains an isometric copy of every separable metric space; (3) every isometry between two finite…

We establish universality and ultra-homogeneity of $(\mathcal{U},u_\mathrm{GH})$, the collection of all compact ultrametric spaces endowed with the so-called Gromov-Hausdorff ultrametric. This result also gives rise to a novel construction…

In this paper we study the hyperbolicity in the sense of Gromov of domains in $\mathbb{R}^d$ $(d\geq3)$ with respect to the minimal metric introduced by Forstneri\v{c} and Kalaj. In particular, we prove that every bounded strongly minimally…

Characterisations of metrizable topological spaces or metrizable uniform spaces are well known. A natural counterpart to being metrizable for topological spaces can be expressed in terms of probabilistic metrizability for approach spaces.…

We construct a class of metric spaces whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\omega+k$ for any $k\in\mathbb{N}$, where $\omega$ is the smallest infinite ordinal number and a metric…

It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus…

We introduce the notion of pseudo-cones of metric spaces as a generalization of both of the tangent cones and the asymptotic cones. We prove that the Assouad dimension of a metric space is bounded from below by that of any pseudo-cone of…

A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces, we show that a countable ultrametric…

We show in ZF that: (i) Every subcompact metrizable space is completely metrizable, and every completely metrizable space is countably subcompact. (ii) A metrizable space X=(X,T) is countably compact iff it is countably subcompact relative…

In this note we prove that every metric space $(X, d)$ of asymptotic dimmension at most $n$ is coarsely equivalent to a metric space $(Y, D)$ that satisfies the following property of Nagata: For every $n+2$ points $y_1,..., y_{n+2}$ in $Y$…

We show that a quasi-geodesic in an injective metric space is Morse if and only if it is strongly contracting. Since mapping class groups and, more generally, hierarchically hyperbolic groups act properly and coboundedly on injective metric…

We build an example of a metric space with transfinite asymptotic dimension $2\omega$.

It is known that hyperbolic spaces have strict negative type, a condition on the distances of any finite subset of points. We show that they have strong negative type, a condition on every probability distribution of points (with integrable…

We characterize Gromov hyperbolicity of the quasihyperbolic metric space (\Omega,k) by geometric properties of the Ahlfors regular length metric measure space (\Omega,d,\mu). The characterizing properties are called the Gehring--Hayman…

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.

In a recent paper \cite{Temme:2021:AKH} new asymptotic expansions are given for the Kummer functions $M(a,b,z)$ and $U(a,b+1,z)$ for large positive values of $a$ and $b$, with $z$ fixed and special attention for the case $a\sim b$. In this…

In the space $\mathbb U^4$ of cubic forms of surfaces, regarded as a $G$-space and endowed with a natural invariant metric, the ratio of the volumes of those representing umbilic points with negative to those with positive indexes is…

By a geodesic subspace of a metric space $X$ we mean a subset $A$ of $X$ such that any two points in $A$ can be connected by a geodesic in $A$. It is easy to check that a geodesic metric space $X$ is an $\mathbb{R}$-tree (that is, a…

In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying the Gromov's $4$-point condition) while the intersection of any two metric balls therein does not either "look like" a ball or has…