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On the chromatic number of Euclidean space and the Borsuk problem. (English. Russian original) Zbl 1291.05073

Math. Notes 83, No. 4, 579-582 (2008); translation from Mat. Zametki 83, No. 4, 636-639 (2008).
Summary: The article reports on the chromatic number of an Euclidean space and the Borsuk problem in the U.S. The Borsuk number \(f(n)\) means the minimal number of parts into which one can divide an arbitrary bounded set of positive diameter so that the diameter of each part will be less than that of the original set. Discussed are details of the issue.

MSC:

05C15 Coloring of graphs and hypergraphs
52C10 Erdős problems and related topics of discrete geometry
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References:

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