Related papers: Introduction to metric spaces with dilations

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

We give a short introduction to the theory of modular metric spaces. This is a corrected version of the paper [1], which had some errors. We are grateful to V. V. Chistyakov for bringing these to our attention.

The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.

Some examples and basic properties of ultrametric spaces are briefly discussed.

This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.

This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…

This is an introductory article to the theory of multiple gaps.

A method of induction the distances with Hilbert structure is proposed. Some properties of the method are studied. Typical examples of corresponding metric spaces are discussed. Key words: Hilbert spaces; metric spaces; isometric embedding…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric…

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…

This article describes a structure that metric spaces can be equipped with so that they resemble normed vector spaces and examines necessary and sufficient conditions for the existence of such a structure on a general metric space.

These lectures are a brief introduction to supersymmetry.

A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a…

In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…

In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…

Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…