Coloring \({\mathbb R}^n\) (Q2759050)
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scientific article; zbMATH DE number 1680708
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Coloring \({\mathbb R}^n\) |
scientific article; zbMATH DE number 1680708 |
Statements
10 December 2001
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graph coloring
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Euclidean spaces
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Coloring \({\mathbb R}^n\) (English)
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It is shown that there exists a function \(\varphi:{\mathbb R}^n\to\omega\) such that for any isometry \(\alpha:{\mathbb R}^n\to {\mathbb R}^n\) the restriction of \(\varphi\) to \(\alpha[{\mathbb Q}^n]\) is a bijection onto \(\omega\). This theorem, generalizing the reviewer's result for \(n=2\) [\textit{P. Komjáth}: ``A coloring result for the plane'', J. Appl. Anal. 5, 113-117 (1999; Zbl 0933.03053)] is further extended to certain subrings of \({\mathbb R}\).
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