Discontinuous groups in some metric and nonmetric spaces
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.
scientific article; zbMATH DE number 3951440