Why is space three-dimensional and how may groups be seen?
type: Item
instance of: scholarly article
title: Why is space three-dimensional and how may groups be seen?
zbMATH Open document ID: 0588.57011
DOI: 10.1007/BF00046586
published in: Acta Applicandae Mathematicae
publication date: 1986-01-01T00:00:00Z
review text: This paper contains two applications of tolerance space theory. The first is a speculative application of the result [see \textit{A. B. Sossinskij}, ibid. 5, 137-167 (1986; see the preceding review)] that tolerance dimension can only take the values 0, 1, 2, or 3. This is used to ''justify'' the three dimensionality of the visual world. The second application introduces the notion of the group crystal associated to a set \(\{H_ i\}\), \(i\in I\), of subgroups of a group G. This is a tolerance space T defined on the set of right cosets of the \(H_ i\) in G. Two cosets \(aH_ i\) and \(bH_ i\) are within tolerance of each other if their intersection is nonempty. The idea is illustrated with a discussion of two generator groups.
Mathematics Subject Classification ID: 57M99
Mathematics Subject Classification ID: 91E30
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 94A40
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20H15
zbMATH DE Number: 3944854
zbMATH Keywords: tolerance space
zbMATH Keywords: tolerance dimension
zbMATH Keywords: group crystal
zbMATH Keywords: two generator groups
author: A. M. Vinogradov
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
cites work: Tolerance space theory and some applications
cites work: Q3207176
description: scientific article; zbMATH DE number 3944854