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On a problem of Erdős concerning decompositions of the plane

Published online by Cambridge University Press:  24 October 2008

Roy O. Davies
Roy O. Davies
Affiliation:
University of Leicester
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Extract

Sierpiński ((6), (7)) proved that the continuum hypothesis implies the following proposition:

Euclidean space E3 can be decomposed into three sets Si (i = 1, 2, 3) such that, for some three straight lines Di in E3, the intersection of each line parallel to Di with the corresponding set Si is finite.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 33 - 36
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

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