Related papers: An introduction to the geometry of ultrametric spa…

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

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

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

These lectures are a brief introduction to supersymmetry.

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.

The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…

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

We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric…

This paper gives a short introduction into the metric theory of spaces with dilations.

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…

We describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.

This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…

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…

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

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…

This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.

The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.

We discuss domestic affairs of metric spaces, keeping away from any extra structure. Topics include universal spaces, injective spaces, Hausdorff and Gromov--Hausdorff convergences, and ultralimits.

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

The paper deals with pretangent spaces to general metric spaces. An ltrametricity criterion for pretangent spaces is found and it is closely related to the metric betweenness in the pretangent spaces.