Related papers: Introduction to metric spaces with dilations
The present article studies combinatorial tilings of Euclidean or spherical spaces by polytopes, serving two main purposes: first, to survey some of the main developments in combinatorial space tiling; and second, to highlight some new and…
This is an expository paper (in Spanish) about the metric approximation of groups.
In this paper, we introduce round and sleek topological spaces and study their properties.
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
This short survey has been prepared in connection with the workshop on discrete metric spaces and their applications at Princeton, August, 2003, and tries to convey some of the ways that one might look at functions on metric spaces in…
We study the concept of cone metric space in the context of ordered vector spaces by setting up a general and natural framework for it.
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
In a recent survey paper we introduced one-sided multipliers between two different operator spaces. Here we give some basic theory for these maps.
The paper is an introduction to intuitionistic mathematics.
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
A definition of space-time metric deformations on an $n$-dimensional manifold is given. We show that such deformations can be regarded as extended conformal transformations. In particular, their features can be related to the perturbation…
We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.
The purpose of this brief article is to clarify certain distortions of the history of ideas about the quantum theory of de Sitter space that have appeared in recent literature.
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…