Related papers: Coarse spaces over the ages
Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures as a large-scale counterpart of uniformities. In the literature,…
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.
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
In this paper we try to organize machine teaching as a coherent set of ideas. Each idea is presented as varying along a dimension. The collection of dimensions then form the problem space of machine teaching, such that existing teaching…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
This chapter discusses a general design approach to planning computer experiments, which seeks design points that fill a bounded design region as uniformly as possible. Such designs are broadly referred to as space-filling designs.
The main purpose of this paper is to introduce and study the primal-proximity spaces. Also, we define two new operators via primal proximity spaces and investigate some of their fundamental properties. In addition, we obtain a new topology,…
John Roe \cite{Roe lectures} introduced coarse structures for arbitrary sets $X$ by considering subsets of $X\times X$. That definition, while natural for analysts, is a bit more difficult to digest for topologists and geometers. In this…
This paper gives a short introduction into the metric theory of spaces with dilations.
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
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…
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…
The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the…
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.
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a (potentially) high-dimensional space. Based on our…