Borel subrings of the reals
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American Mathematical Society
Abstract
A Borel (or even analytic) subring of R either has Hausdorff dimension 0 or is all of R. Extensions of the method of proof yield (among other things) that any analytic subring of C having positive Hausdorff dimension is equal to either R or C.
Description
First published in Proceedings of the American Mathematical Society in volume 131 and issue 4, published by the American Mathematical Society.
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Citation
G. A. Edgar and Chris Miller, "Borel subrings of the reals," Proceedings of the American Mathematical Society 131, no. 4 (2003), doi:10.1090/S0002-9939-02-06653-4