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Borel subrings of the reals
Authors:
G. A. Edgar and Chris Miller
Journal:
Proc. Amer. Math. Soc. 131 (2003), 1121-1129
MSC (2000):
Primary 28A78; Secondary 03E15, 11K55, 12D99, 28A05
Posted:
June 12, 2002
MathSciNet review:
1948103
Full-text PDF Free Access
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Additional Information
Abstract: A Borel (or even analytic) subring of  either has Hausdorff dimension  or is all of  . Extensions of the method of proof yield (among other things) that any analytic subring of  having positive Hausdorff dimension is equal to either  or  .
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Additional Information
G. A. Edgar
Affiliation:
Department of Mathematics, The Ohio State University, 231 West Eighteenth Avenue, Columbus, Ohio 43210
Email:
edgar@math.ohio-state.edu
Chris Miller
Affiliation:
Department of Mathematics, The Ohio State University, 231 West Eighteenth Avenue, Columbus, Ohio 43210
Email:
miller@math.ohio-state.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06653-4
PII:
S 0002-9939(02)06653-4
Keywords:
Borel subring,
Borel subfield,
Hausdorff dimension,
Erd\H{o}s,
Volkmann,
Suslin sets,
analytic sets
Received by editor(s):
October 29, 2001
Posted:
June 12, 2002
Additional Notes:
Research of the second author was supported by NSF grant no. DMS-9988855
Communicated by:
David Preiss
Article copyright:
© Copyright 2002 American Mathematical Society
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