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On three sets with no point in common

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

P. R. Scott
P. R. Scott
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia.
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Extract

From time to time results about partitioning a given set into subsets have been established. (See for example [2], [3].) We consider here the reverse problem of forming the union of three sets in a certain best possible way. For simplicity we work in Euclidean n-space, En. Let mX denote the measure of the set X.

MSC classification

Secondary: 52A10: Convex sets in $2$ dimensions (including convex curves)

Information

Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978 , pp. 17 - 23
Copyright
Copyright © University College London 1978

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References

1.Benson, R. V., Euclidean geometry and convexity (McGraw-Hill, New York, 1966).Google Scholar
2.Buck, Ellen F. and Buck, R. C.. “Equipartition of convex sets.”, Math. Magazine, 22 (1949), 195–198.CrossRefGoogle Scholar
3.Eggleston, H. G.. Problems in Euclidean space (Pergamon, London, 1957).Google Scholar
4.Yaglom, I. M. and Boltyanskü, V. G.. Convex figures (Holt, Rinehart and Winston, New York, 1961).Google Scholar