相关论文: An introduction to the geometry of metric spaces

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

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

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

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.

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…

These are some basic notes concerning Holder and Lipschitz classes on metric spaces.

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

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.

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…

Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.

These notes deal with metric spaces, Hausdorff measures and dimensions, Lipschitz mappings, and related topics. The reader is assumed to have some familiarity with basic analysis, which is also reviewed.

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.

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…

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

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…

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…

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.