Topological group foundations of rigid space geometry
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- by Deane Montgomery and Leo Zippin
- Trans. Amer. Math. Soc. 48 (1940), 21-49
- DOI: https://doi.org/10.1090/S0002-9947-1940-0002148-9
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References
- Alexandroff and Hopf, Topologie I, Berlin, 1935.
Cartan, La Théorie des Groupes Finis et Continus et l’Analysis Situs, Mémorial des Sciences Mathématiques, vol. 42.
- Stewart S. Cairns, An axiomatic basis for plane geometry, Trans. Amer. Math. Soc. 35 (1933), no. 1, 234–244. MR 1501680, DOI 10.1090/S0002-9947-1933-1501680-2 Hilbert, Grundlagen der Geometrie, 7th edition, 1930. —, 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. 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.
- Deane Montgomery and Leo Zippin, Periodic one-parameter groups in three-space, Trans. Amer. Math. Soc. 40 (1936), no. 1, 24–36. MR 1501864, DOI 10.1090/S0002-9947-1936-1501864-6
- Deane Montgomery and Leo Zippin, Compact Abelian transformation groups, Duke Math. J. 4 (1938), no. 2, 363–373. MR 1546057, DOI 10.1215/S0012-7094-38-00428-4 —, Non-abelian compact connected groups of three-space, American Journal of Mathematics, vol. 61 (1939), pp. 375-387.
- Deane Montgomery and Leo Zippin, Topological transformation groups. I, Ann. of Math. (2) 41 (1940), 778–791. MR 2529, DOI 10.2307/1968858
- Deane Montgomery and Leo Zippin, A theorem on the rotation group of the two-sphere, Bull. Amer. Math. Soc. 46 (1940), 520–521. MR 2147, DOI 10.1090/S0002-9904-1940-07251-9
- P. A. Smith, The topology of transformation groups, Bull. Amer. Math. Soc. 44 (1938), no. 8, 497–514. MR 1563784, DOI 10.1090/S0002-9904-1938-06785-7 Veblen and Young, Projective Geometry, vol. 2.
Bibliographic Information
- © Copyright 1940 American Mathematical Society
- 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