Related papers: Asymptotically Scattered Spaces

Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the so called gap of a finite metric space of strict…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained…

A metric space is plastic if all its non-expansive bijections are isometries. We prove three main results: (1) every countable dense subspace of a normed space is not plastic, (2) every $k$-crowded separable metric space contains a plastic…

The space of $G$-invariant metrics on a homogeneous space $G/H$ is in one-to-one correspondence with the set of inner products on the tangent space $\fr{m}\cong T_{{\it o}}(G/H)$, which are invariant under the isotropy representation. When…

The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…

Within a category $\mathtt{C}$, having objects $\mathtt{C}_0$, it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic they are. We introduce pseudo-metrics $d:\mathtt{C}_0 \times…

We define a notion of asymptotically spherical topological groups, which says that spheres of large radius with respect to any maximal length function are still spherical with respect to any other maximal length function. This is a…

In this paper we combine the notions of partial metric spaces with negative distances, $G_p$-metric spaces and n-metric spaces together into one structure called the partial n-metric spaces. These are generalizations of all the said…

We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of…

We study invariant and bi-invariant metrics on groups focusing on finite groups $G$. We show that non-equivalent (bi) invariant metrics on $G$ are in 1-1 correspondence with unitary symmetric (conjugate) partitions on $G$. To every metric…

We derive an asymptotic expansion for two-dimensional displacement field associated to thin elastic inhomogeneities having no uniform thickness. Our derivation is rigorous and based on layer potential techniques. We extend these techniques…

This note is devoted to proving the following result: given a compact metrizable group G, there is a compact metric space K such that G is isomorphic (as a topological group) to the isometry group of K.

In this paper, we define notions of $P_{Z}(S)$-metric and $P_{Z}(S)$-metric space and we show that every $P_{Z}(S)$-metric Space, analogous to an ordinary metric space and generally, a $\Lambda$-metric space, is a topological space, and in…

We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic…

Our aim in this paper is to prove some interesting fixed point theorems for the class of asymptotically $T$-regular mappings in the framework of preordered modular G-metric spaces. Our results are novel and generalizes several know results.…

This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft…

We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the…

We characterize 1-complemented subspaces of finite codimension in strictly monotone one-$p$-convex, $2<p<\infty,$ sequence spaces. Next we describe, up to isometric isomorphism, all possible types of 1-unconditional structures in sequence…

In this paper we give some relationship between G-metric spaces, partial metric spaces and GP-metric spaces.