A decomposition theorem for $\textbf {R}^ n$
HTML articles powered by AMS MathViewer
- by Péter Komjáth PDF
- Proc. Amer. Math. Soc. 120 (1994), 921-927 Request permission
Abstract:
${{\mathbf {R}}^n}$ is the union of countably many sets, none containing two points a rational distance apart.References
- Jack Ceder, Finite subsets and countable decompositions of Euclidean spaces, Rev. Roumaine Math. Pures Appl. 14 (1969), 1247–1251. MR 257307
- Roy O. Davies, Partitioning the plane into denumberably many sets without repeated distances, Proc. Cambridge Philos. Soc. 72 (1972), 179–183. MR 294592, DOI 10.1017/s0305004100046983
- P. Erdős, Set-theoretic, measure-theoretic, combinatorial, and number-theoretic problems concerning point sets in Euclidean space, Real Anal. Exchange 4 (1978/79), no. 2, 113–138. MR 533932, DOI 10.2307/44151159
- P. Erdős and A. Hajnal, On chromatic number of graphs and set-systems, Acta Math. Acad. Sci. Hungar. 17 (1966), 61–99. MR 193025, DOI 10.1007/BF02020444
- P. Erdős and P. Komjáth, Countable decompositions of $\textbf {R}^2$ and $\textbf {R}^3$, Discrete Comput. Geom. 5 (1990), no. 4, 325–331. MR 1043714, DOI 10.1007/BF02187793
- Péter Komjáth, Tetrahedron free decomposition of $\textbf {R}^3$, Bull. London Math. Soc. 23 (1991), no. 2, 116–120. MR 1122894, DOI 10.1112/blms/23.2.116
- James H. Schmerl, Partitioning Euclidean space, Discrete Comput. Geom. 10 (1993), no. 1, 101–106. MR 1215326, DOI 10.1007/BF02573966
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 921-927
- MSC: Primary 04A20; Secondary 52C10
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169038-0
- MathSciNet review: 1169038