相关论文: What is a metric space?

The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We develop…

This note tries to give an answer to the following question: Is there a sufficiently rich class of metric vector spaces such that sufficiently large spaces of continuous linear maps between them are metrizable?

Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpi\'nski and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric…

We give a brief survey of many of the high-lights of our present understanding of the young subject of quantum metric spaces, and of quantum Gromov-Hausdorff distance between them. We include examples.

We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.

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…

"An invariant of metric spaces under bornologous equivalences" gives an invariant and "A coarse invariant" extends the invariant to coarse equivalences. In both papers the invariant is defined for a class of metric spaces called sigma…

The main purpose of this manuscript is to provide a short proof of the metrizability of $\mathcal{F}$-metric spaces introduced by Jleli and Samet in \cite[\, Jleli, M. and Samet, B., On a new generalization of metric spaces, J. Fixed Point…

Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We…

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

Basic properties of Hausdorff content, dimension, and measure of subsets of metric spaces are discussed, especially in connection with Lipschitz mappings and topological dimension.

It is proved that a metric space is sober, as an approach space, if and only if it is Smyth complete.

In this paper, we show that the metric space Q is a positively-curved space (PC-space) in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map of Q. Then we give a stratification of this metric…

We develop an analog to the ends of a metric space for the category of coarse metric spaces and show that it is equivalent to a previously defined coarse invariant.

We investigate several boundedness properties of function spaces considered as uniform spaces.

In this paper, using a more generalized inequality instead of triangle inequality, the notion of \theta-metric space is introduced. Some important properties of induced topology by such spaces are presented. Also, Banach and Caristi type…

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…

Property($M$) in separable Banach spaces has played an important role in metric fixed point theory. This paper explores some of the Banach space properties that can be associated with Property($M$) and Property($M^*$).

This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…

The main purpose of this paper is to introduce and study the primal-proximity spaces. Also, we define two new operators via primal proximity spaces and investigate some of their fundamental properties. In addition, we obtain a new topology,…