Related papers: Some basic aspects of analysis on metric and ultra…
Some examples and basic properties of ultrametric spaces are briefly discussed.
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.
Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.
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.
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.
The question in the title is discussed briefly, with emphasis on a few basic examples and their 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…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
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 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.
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes…
Here we look at some geometric properties related to connectedness and topological dimension 0, especially in connection with norms on vector spaces over fields with absolute value functions, which may be non-archimedian.
We describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.
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…
Basic properties of Hausdorff content, dimension, and measure of subsets of metric spaces are discussed, especially in connection with Lipschitz mappings and topological dimension.
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…