Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Analytic subgroups of the reals

Author: Miklós Laczkovich
Journal: Proc. Amer. Math. Soc. 126 (1998), 1783-1790
MSC (1991): Primary 04A15
MathSciNet review: 1443837
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every analytic proper subgroup of the reals can be covered by an $F_{\sigma }$ null set. We also construct a proper Borel subgroup $G$ of the reals that cannot be covered by countably many sets $A_{i}$ such that $A_{i} +A_{i}$ is nowhere dense for every $i.$

References [Enhancements On Off] (What's this?)

  • 1. K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
  • 2. John C. Oxtoby, Measure and category. A survey of the analogies between topological and measure spaces, Springer-Verlag, New York-Berlin, 1971. Graduate Texts in Mathematics, Vol. 2. MR 0393403
  • 3. Gy. Petruska, On Borel sets with small cover: a problem of M. Laczkovich, Real Anal. Exchange 18 (1992/93), no. 2, 330–338. MR 1228398
    György Petruska, Errata to: “On Borel sets with small cover: a problem of M. Laczkovich”, Real Anal. Exchange 19 (1993/94), no. 1, 58. MR 1268831
  • 4. Sławomir Solecki, Covering analytic sets by families of closed sets, J. Symbolic Logic 59 (1994), no. 3, 1022–1031. MR 1295987,

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 04A15

Retrieve articles in all journals with MSC (1991): 04A15

Additional Information

Miklós Laczkovich
Affiliation: Department of Analysis, Eötvös Loránd University, Budapest, Muzeum krt. 6-8, Hungary 1088

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
Article copyright: © Copyright 1998 American Mathematical Society