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Transactions of the American Mathematical Society

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Topological group foundations of rigid space geometry


Authors: Deane Montgomery and Leo Zippin
Journal: Trans. Amer. Math. Soc. 48 (1940), 21-49
MSC: Primary 20.0X
DOI: https://doi.org/10.1090/S0002-9947-1940-0002148-9
MathSciNet review: 0002148
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  • [1] Alexandroff and Hopf, Topologie I, Berlin, 1935.
  • [2] Cartan, La Théorie des Groupes Finis et Continus et l'Analysis Situs, Mémorial des Sciences Mathématiques, vol. 42.
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  • [4] Hilbert, Grundlagen der Geometrie, 7th edition, 1930.
  • [5] -, Über die Grundlagen der Geometrie, Mathematische Annalen, vol. 56, pp. 381-422. This article is reprinted as appendix IV, pp. 178-230, in the edition of Hilbert's book referred to above.
  • [6] Kerékjártó, On a geometrical theory of continuous groups, II. Euclidean and hyperbolic groups of three dimensional space, Annals of Mathematics, (2), vol. 29, pp. 169-179.
  • [7] Montgomery and Zippin, Periodic one-parameter groups in three-space, these Transactions, vol. 40 (1936), pp. 24-36. MR 1501864
  • [8] -, Compact abelian transformation groups, Duke Mathematical Journal, vol. 4 (1938), pp. 363-373. MR 1546057
  • [9] -, Non-abelian compact connected groups of three-space, American Journal of Mathematics, vol. 61 (1939), pp. 375-387.
  • [10] -, Topological transformation groups I, Annals of Mathematics, (2), vol. 41 (1940). MR 0002529 (2:70b)
  • [11] -, A theorem on the rotation group of the two-sphere, Bulletin of the American Mathematical Society, vol. 46 (1940), pp. 520-521. MR 0002147 (2:6f)
  • [12] P. A. Smith, The topology of transformation groups, Bulletin of the American Mathematical Society, vol. 44 (1938), pp. 497-514. MR 1563784
  • [13] Veblen and Young, Projective Geometry, vol. 2.

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DOI: https://doi.org/10.1090/S0002-9947-1940-0002148-9
Article copyright: © Copyright 1940 American Mathematical Society

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