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Distance Sets

Published online by Cambridge University Press:  20 November 2018

L. M. Kelly
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With each set of points S of a distance space there is associated a set of non-negative real munbers D(S) called the distance set of 5. The number x is an element of D(S) if and only if x is a distance between some pair of points of 5. The number zero is always an element of any distance set and no two distinct elements are equal.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 187 - 194
Copyright
Copyright © Canadian Mathematical Society 1951

References

[1] Aiming, N. H. and Erdös, P., Integral distances, Bull. Amer. Math. Soc., vol. 51 (1945), 598–600.Google Scholar
[2] Blumenthal, L. M., Distance geometries, University of Missouri Studies, vol. 13, no. 2 (1938).Google Scholar
[3] Erdös, P., Integral distances, Bull. Amer. Math. Soc., vol. 51 (1945), 996.Google Scholar
[4] Piccard, S., Sur les ensembles de distances des points d'lune espace euclidean. Mem. Univ. Neuchatel, vol. 13, Secretariat de l'Université, Neuchatel, 1939.Google Scholar
[5] Sierpinski, W., Sur un probléme de M. Lusin. Giornale de Matematiche, 1917.Google Scholar
[6] Steinhaus, H., Sur les distances des points des ensembles de mesure positive, Fundamenta Mathematica, vol. 1 (1920), 93–104.Google Scholar