Hausdorff Dimension, Analytic Sets and Transcendence

G. A. Edgar; Chris Miller

doi:rae/1212763973

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Home > Journals > Real Anal. Exchange > Volume 27 > Issue 1 > Article

2001/2002 Hausdorff Dimension, Analytic Sets and Transcendence

G. A. Edgar, Chris Miller

Real Anal. Exchange 27(1): 335-340 (2001/2002).

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Abstract

Every analytic real closed proper sub-field of $\mathbb R$ has Hausdorff dimension zero. Equivalently, every analytic set of real numbers having positive Hausdorff dimension contains a transcendence base for $\mathbb R$.

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G. A. Edgar. Chris Miller. "Hausdorff Dimension, Analytic Sets and Transcendence." Real Anal. Exchange 27 (1) 335 - 340, 2001/2002.

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Published: 2001/2002

First available in Project Euclid: 6 June 2008

zbMATH: 1082.28002

MathSciNet: MR1887864

Subjects:

Primary: 03C64 , 03E15 , 12L12 , 28A05 , 28A78

Keywords: analytic sets , Borel subrings , Hausdorff dimension , Real Closed Fields

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Vol.27 • No. 1 • 2001/2002

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G. A. Edgar, Chris Miller "Hausdorff Dimension, Analytic Sets and Transcendence," Real Analysis Exchange, Real Anal. Exchange 27(1), 335-340, (2001/2002)

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