Related papers: What is a metric space?

Let $\mathfrak{M}$ be a class of metric spaces. A metric space $Y$ is minimal $\mathfrak{M}$-universal if every $X\in\mathfrak{M}$ can be isometrically embedded in $Y$ but there are no proper subsets of $Y$ satisfying this property. We find…

We find necessary and sufficient conditions under which an arbitrary metric space $X$ has a unique pretangent space at the marked point $a\in X$. Key words: Metric spaces; Tangent spaces to metric spaces; Uniqueness of tangent metric…

In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.

This short survey has been prepared in connection with the workshop on discrete metric spaces and their applications at Princeton, August, 2003, and tries to convey some of the ways that one might look at functions on metric spaces in…

In this paper, we give an interesting extension of the partial S-metric space which was introduced [4] to the M_s-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Ms-metric space under…

The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…

The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…

We use the trimming transformations to study the tight span of a metric space.

We introduce the concept of protometric and present some properties of protometrics.

Here Lipschitz conditions are used as a primary tool, for studying curves in metric spaces in particular.

These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.

In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…

We give a short review of a construction of Frink to obtain a metric space from a quasi-metric space. By an example we illustrate the limits of the construction.

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.

We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces appearing in fractal geometry. For doubling tiling spaces, we…

We present a complete study of measure-theoretic area formulas in metric spaces, providing different measurability conditions.

We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.

Property A introduced by Guoliang Yu is an amenability-type property for metric spaces. In this article, we study property A for uniformly locally finite coarse spaces. Main examples of coarse spaces are a metric space, a set equipped with…

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 classify the metric spaces that can be approximated by finite homogeneous ones.