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An approximate theorem for Borsuk's conjecture

Published online by Cambridge University Press:  24 October 2008

Robert Knast
Robert Knast
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Poznań Branch
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Extract

In 1933 Borsuk(2) made the following conjecture: Every bounded set of points in Euclidean n-space En can be represented as the union of n + 1 sets of smaller diameter. He proved it for n = 2. Hadwiger (5) proved Borsuk's conjecture assuming the additional condition that the surface of the set is sufficiently smooth. On the other hand, up to now the conjecture has been proved for n ≤ 3 only (3, 4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 1 , January 1974 , pp. 75 - 76
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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