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The Hausdorff dimension of certain sets of singular n-tuples

Published online by Cambridge University Press:  24 October 2008

Bryan P. Rynne
Bryan P. Rynne
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee DDl 4HN, Scotland
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Extract

In the paper [3] we obtained a lower bound for the Hausdorff dimension of certain sets of singular n-tuples in ℝn. In this paper we will obtain an upper bound for the dimension of these sets. These two bounds are not sharp enough to yield the exact dimension of all the sets considered but they do yield the dimension of the set of ‘highly singular’ (in a sense to be made precise below) n-tuples.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 1 , July 1990 , pp. 105 - 110
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Baker, R. C.. Singular n-tuples and Hausdorff dimension. Math. Proc. Cambridge Philos. Soc. 81 (1977), 377–385.CrossRefGoogle Scholar
[2]Cassels, J. W. S.. An Introduction to Diophantine Approximation (Cambridge University Press, 1965).Google Scholar
[3]Rynne, B. P.. A lower bound for the Hausdorff dimension of sets of singular n-tuples. Math. Proc. Cambridge Philos. Soc. 107 (1990), 387–394.CrossRefGoogle Scholar