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Analytic subgroups of the reals
Author(s):
Miklós
Laczkovich
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1783-1790.
MSC (1991):
Primary 04A15
MathSciNet review:
1443837
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Abstract:
We prove that every analytic proper subgroup of the reals can be covered by an  null set. We also construct a proper Borel subgroup  of the reals that cannot be covered by countably many sets  such that  is nowhere dense for every 
References:
- 1.
- K. Kuratowski, Topology, Vol. I. Academic Press, 1966. MR 36:840
- 2.
- J. C. Oxtoby, Measure and Category. Springer, 1971. MR 52:14213
- 3.
- Gy. Petruska, On Borel sets with small cover, Real Analysis Exchange 18 (1992-93) (2), 330-338. MR 95g:28003a
- 4.
- S. Solecki, Covering analytic sets by families of closed sets, Journal of Symbolic Logic 59 (1994), 1022-1031. MR 95g:54033
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Additional Information:
Miklós
Laczkovich
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Muzeum krt. 6-8, Hungary 1088
Email:
laczk@cs.elte.hu
DOI:
10.1090/S0002-9939-98-04241-5
PII:
S 0002-9939(98)04241-5
Received by editor(s):
February 20, 1996
Received by editor(s) in revised form:
November 21, 1996
Additional Notes:
This work was completed when the author had a visiting position at the Mathematical Institute of the Hungarian Academy of Sciences. Also supported by the Hungarian National Foundation for Scientific Research, Grant T016094.
Communicated by:
Andreas R. Blass
Copyright of article:
Copyright
1998,
American Mathematical Society
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