Abstract
Let the sets A1, A2,...,An+1, form a covering of the n-dimensional euclidean space Rn (n>1). Then among these sets can be found a set Ai containing, for every d>0, a pair of points such that the distance between them is equal to d.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
H. Hadwiger, “Ein Überdeckungssatz für den Euklidischen Raum,” Portugaliae Math.,4, 140–144 (1944).
D. G. Larman, “On the realization of distances within decomposition in Rn,” J. London Math. Soc.,42, 744–749 (1967).
H. Hadwiger and H. Debrunner, Combinatorial Geometry in the Plane [Russian translation], Moscow (1965).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 7, No. 3, pp. 319–323, March, 1970.
Rights and permissions
About this article
Cite this article
Raiskii, D.E. Realization of all distances in a decomposition of the space Rn into n+1 parts. Mathematical Notes of the Academy of Sciences of the USSR 7, 194–196 (1970). https://doi.org/10.1007/BF01093113
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01093113