Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-27T20:06:01.503Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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