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A maximal Gross-Stadje number in the Euclidean plane

Published online by Cambridge University Press:  17 April 2009

F. Pillichshammer
F. Pillichshammer
Affiliation:
Institut für Mathematik, Universität Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria, e-mail: Friedrich.Pillichshammer@sbg.ac.at
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Abstract

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Let X be a compact, connected Hausdorff space and f a real valued, symmetric, continuous function on X × X. Then the Gross-Stadje number r (X, f) is the unique real number with the property that for each positive integer n and for all (not necessarily distinct) x1,…,xn in X, there exists some x in X such that . This paper solves the following open question in distance geometry: What is the least upper bound g2(R2) of r (X, d2), where X ranges over all compact, connected subsets of the Euclidean plane with diameter one and where d2 denotes the squared, Euclidean distance. We show: .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 109 - 119
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

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