Klotzek, Benno Discontinuous groups in some metric and nonmetric spaces. (English) Zbl 0592.51021 Beitr. Algebra Geom. 21, 57-66 (1986). 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. Reviewer: O.Bottema Cited in 2 Documents MSC: 51N25 Analytic geometry with other transformation groups 51M10 Hyperbolic and elliptic geometries (general) and generalizations 57S30 Discontinuous groups of transformations 54E35 Metric spaces, metrizability Keywords:discontinuous groups of metric spaces; pseudo-Euclidean plane; normed plane PDFBibTeX XMLCite \textit{B. Klotzek}, Beitr. Algebra Geom. 21, 57--66 (1986; Zbl 0592.51021) Full Text: EuDML