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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Metric foundations of geometry. I


Author: Garrett Birkhoff
Journal: Trans. Amer. Math. Soc. 55 (1944), 465-492
MSC: Primary 48.0X
MathSciNet review: 0010393
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  • [1] Garrett Birkhoff, Lattice theory, American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1961. Revised ed. MR 0123490 (23 #A815)
  • [2] Garrett Birkhoff, Metric foundations of geometry, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 402–406. MR 0004472 (3,12c)
  • [1] L. Blumenthal Distance geometries, University of Missouri Press, 1938.
  • [1] Herbert Busemann, On Leibniz’s definition of planes, Amer. J. Math. 63 (1941), 101–111. MR 0003707 (2,258e)
  • [2] Herbert Busemann, Metric Methods in Finsler Spaces and in the Foundations of Geometry, Annals of Mathematics Studies, no. 8, Princeton University Press, Princeton, N. J., 1942. MR 0007251 (4,109e)
  • [1] J. L. Coolidge The elements of non-Euclidean geometry, Oxford, 1909.
  • [1] T. L. Heath The thirteen books of Euclid's elements, Cambridge University Press, 1908, 1926.
  • [1] D. Hilbert Grundlagen der Geometrie, 7th ed., Teubner, 1930.
  • [1] A. Kolmogoroff Zur topologisch-gruppentheoretischen Begrundung der Geometrie, Nachr. Ges. Wiss. Göttingen (1930) pp. 208-210.
  • [1] Karl Menger, Untersuchungen über allgemeine Metrik, Math. Ann. 100 (1928), no. 1, 75–163 (German). MR 1512479, http://dx.doi.org/10.1007/BF01448840
  • [2] Karl Menger, New foundations of projective and affine geometry, Ann. of Math. (2) 37 (1936), no. 2, 456–482. In collaboration with Franz Alt and Otto Schreiber. MR 1503293, http://dx.doi.org/10.2307/1968458

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1944-0010393-5
PII: S 0002-9947(1944)0010393-5
Article copyright: © Copyright 1944 American Mathematical Society