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Subfields of R with arbitrary Hausdorff dimension

Published online by Cambridge University Press:  31 March 2016

R. DANIEL MAULDIN
R. DANIEL MAULDIN*
Affiliation:
5383 Renaissance Avenue, San Diego, CA 92122, U.S.A. e-mail: [email protected]
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Abstract

Assuming CH, the continuum hypothesis, holds we show, by completing an attack first discovered by Roy Davies, that for each α between 0 and 1 there is a subring, in fact a subfield, of R with Hausdorff dimension α.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 1 , July 2016 , pp. 157 - 165
Copyright
Copyright © Cambridge Philosophical Society 2016 

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