Borsuk's problem and the chromatic numbers of some metric spaces (Q2784519)
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scientific article; zbMATH DE number 1732413
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Borsuk's problem and the chromatic numbers of some metric spaces |
scientific article; zbMATH DE number 1732413 |
Statements
Borsuk's problem and the chromatic numbers of some metric spaces (English)
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4 June 2002
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bounded \(d\)-dimensional set
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chromatic number
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0.9968644
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0.9533494
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0.9193032
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0.9066962
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0.89906496
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0.89022404
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The paper contains various results pertaining to two problems of combinatorial geometry: Borsuk's problem on partitions of an arbitrary bounded \(d\)-dimensional set of non-zero diameter into parts of smaller diameter and the problem of finding chromatic numbers of some metric spaces. The author presents an exposition of the general method for constructing counterexamples to Borsuk's conjecture and obtaining lower bounds for the minimum number of parts of smaller diameter as well as for chromatic numbers of real and rational spaces.
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