Abstract
Because of new applications, the research of discontinuous groups with respect to different geometries has made considerable progress. One can state that conditions which all characterize the same discontinuous motion groups in Euclidean spaces of the same finite dimension define different classes of discontinuous transformation groups in other geometries. Moreover in the following section 2, sixteen conditions are discribed which define only eight conditions in metric spaces (section 3). Finally, there are results about new classes of so-called Di — and D i ′ -discontinuous motion groups of the Euclidean geometry.
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