Discontinuous groups in some metric and nonmetric spaces
type: Item
instance of: scholarly article
title: Discontinuous groups in some metric and nonmetric spaces
zbMATH Open document ID: 0592.51021
author: Benno Klotzek
published in: Beiträge zur Algebra und Geometrie
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138325
review text: The author accepts the definition of a discontinuous group as given by Hilbert and Cohn-Vossen which comes to this: There are only finite many points equivalent under the map group in any bounded domain. In the first section of the paper conditions are described which all characterize the discontinuous groups of certain metric spaces. In the following sections the groups under consideration are essentially studied for the cases of the normed and the pseudo-Euclidean plane respectively. In particular, a criterion is given that a normed plane is Euclidean and a criterion of ''badly approximable irrational numbers''. The author emphasises that his work has many relations to that of Minkowski.
Mathematics Subject Classification ID: 51N25
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 3951440
zbMATH Keywords: discontinuous groups of metric spaces
zbMATH Keywords: pseudo-Euclidean plane
zbMATH Keywords: normed plane
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3951440