Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Transitives of betweenness


Authors: Everett Pitcher and M. F. Smiley
Journal: Trans. Amer. Math. Soc. 52 (1942), 95-114
MSC: Primary 56.0X
DOI: https://doi.org/10.1090/S0002-9947-1942-0007099-3
MathSciNet review: 0007099
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Garrett Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications, vol. 25, 1940. MR 0001959 (1:325f)
  • [2] L. M. Blumenthal, Betweenness in metric ptolemaic spaces, Bulletin of the American Mathematical Society, abstract 47-1-66.
  • [3] -, Distance Geometries, The University of Missouri Studies, vol. 13, no. 2 (1938).
  • [4] W. D. Duthie, Segments of ordered sets, these Transactions, vol. 51 (1942), pp. 1-14. MR 0007032 (4:74h)
  • [5] V. Glivenko, Contributions à l'étude des systèmes de choses normées, American Journal of Mathematics, vol. 59 (1937), pp. 941-956. MR 1507294
  • [6] -, Géométrie des systèmes de choses normées, American Journal of Mathematics, vol. 58 (1936), pp. 799-828.
  • [7] E. V. Huntington, A new set of postulates for betweenness with proof of complete independence, these Transactions, vol. 26 (1924), pp. 257-282. MR 1501278
  • [8] E. V. Huntington and J. R. Kline, Sets of independent postulates for betweenness, these Transactions, vol. 18 (1917), pp. 301-325. MR 1501071
  • [9] K. Menger, Untersuchungen über allgemeine Metrik, Mathematische Annalen, vol. 100 (1928), pp. 75-163. MR 1512479
  • [10] Pasch-Dehn, Grundlagen der Geometrie, Berlin, 1926.
  • [11] Gilbert de B. Robinson, The Foundations of Geometry, Mathematical Expositions, Toronto, no. 1, 1940. MR 0002929 (2:135a)
  • [12] I. J. Schoenberg, Metric arcs of vanishing Menger curvature, Annals of Mathematics, (2), vol. 41 (1940), pp. 715-726. MR 0002903 (2:130b)
  • [13] A. Wald, Axiomatik des Zwischenbegriffes in metrischen Räume, Mathematischen Annalen, vol. 104, (1930-1931), pp. 476-484.
  • [14] W. E. van de Walle, On the complete independence of the postulates for betweenness, these Transactions, vol. 24 (1926), pp. 249-256.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 56.0X

Retrieve articles in all journals with MSC: 56.0X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1942-0007099-3
Article copyright: © Copyright 1942 American Mathematical Society

American Mathematical Society