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Arthur Moritz Schoenflies (German: [ˈʃøːnfliːs]; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology.
The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is a notation primarily used to specify point groups in three dimensions. Because a point group alone is completely adequate to describe the symmetry of a molecule , the notation is often sufficient and commonly used for spectroscopy .
Schoenflies (or Schönflies) displacement (or motion) named after Arthur Moritz Schoenflies is a rigid body motion consisting of linear motion in three dimensional space plus one orientation around an axis with fixed direction. [1]
The original formulation of the Schoenflies problem states that not only does every simple closed curve in the plane separate the plane into two regions, one (the "inside") bounded and the other (the "outside") unbounded; but also that these two regions are homeomorphic to the inside and outside of a standard circle in the plane.
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Earlier, Jordan's proof and another early proof by Charles Jean de la Vallée Poussin had already been critically analyzed and completed by Schoenflies (1924). [ 15 ] Due to the importance of the Jordan curve theorem in low-dimensional topology and complex analysis , it received much attention from prominent mathematicians of the first half of ...