$k$-congruence orders for $E_{k}$
HTML articles powered by AMS MathViewer
- by Grattan P. Murphy
- Trans. Amer. Math. Soc. 177 (1973), 405-412
- DOI: https://doi.org/10.1090/S0002-9947-1973-0319059-3
- PDF | Request permission
Abstract:
This paper generalizes the notion of congruence order for metric spaces to k-metric (k-dimensional metric) spaces. The k-congruence order of ${E_k}$ with respect to the class of oriented semi k-metric spaces is determined. An example shows that this result is sharp.References
- Leonard M. Blumenthal, Theory and applications of distance geometry, Oxford, at the Clarendon Press, 1953. MR 0054981
- L. M. Blumenthal, Distance geometry notes, Bull. Amer. Math. Soc. 50 (1944), 235–241. MR 9859, DOI 10.1090/S0002-9904-1944-08121-4 Siegfried Gähler, Untersuchungen über verallgemeinerte m-metrische Raüme. I, Math. Nachr. 40 (1969), 165-189. MR 40 #1989.
- Karl Menger, Untersuchungen über allgemeine Metrik, Math. Ann. 100 (1928), no. 1, 75–163 (German). MR 1512479, DOI 10.1007/BF01448840
- Karl Menger, New Foundation of Euclidean Geometry, Amer. J. Math. 53 (1931), no. 4, 721–745. MR 1506850, DOI 10.2307/2371222
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 177 (1973), 405-412
- MSC: Primary 52A50
- DOI: https://doi.org/10.1090/S0002-9947-1973-0319059-3
- MathSciNet review: 0319059