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The Hausdorff distance between compact convex sets

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

P. McMullen
P. McMullen
Affiliation:
University College London, Gower Street, London. WC1E 6BT
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Abstract

It is shown that every compact convex set in with mean width equal to that of a line segment of length 2 and with Steiner point at the origin is contained in the unit ball. As a consequence, the diameter with respect to the Hausdorff metric of the space of all such sets is 1. There also results a sharp bound for the Hausdorff distance between any two compact convex sets.

MSC classification

Secondary: 52A40: Inequalities and extremum problems

Information

Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 76 - 82
Copyright
Copyright © University College London 1984

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References

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