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Completely stretched sets

Published online by Cambridge University Press:  24 October 2008

J. N. Lillington
J. N. Lillington
Affiliation:
Royal Holloway College
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Extract

Introduction. All the sets X considered in this paper will be compact convex subsets of the Euclidean plane R. We shall require the following definitions. For x, y, z ∈ R let L(x, y, x) denote the minimum of all the lengths of all connected sets containing x, y and z. Define the stretch of x with respect to X to be

and the stretch of X to be

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 1 , January 1974 , pp. 37 - 43
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Eggleston, H. G.On the projection of a plane set of finite linear measure. Acta Math. 99 (1958), 53–91.CrossRefGoogle Scholar
(2)Eggleston, H. G.Convexity (Cambridge University Press, 1958).CrossRefGoogle Scholar
(3)Fujiwara, M. and Kakeya, S.On some problems of maxima and minima for the curve of constant breadth and the un-revolvable curve of the equilateral triangle. Tôhoku Math. J. 11 (1917), 92–110.Google Scholar