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)



Remarks about $ \gamma$-sets and Borel-dense sets

Author: Ireneusz Recław
Journal: Proc. Amer. Math. Soc. 123 (1995), 3523-3525
MSC: Primary 03E50; Secondary 04A15
MathSciNet review: 1273519
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show, assuming Martin's Axiom, that every set of cardinality the continuum containing a Borel-dense set of cardinality less than the continuum is a $ \gamma $-set but is not a hereditarily $ \gamma $-set. This answers a question of D. H. Fremlin and J. Jasinski.

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

  • [1] D. H. Fremlin and J. Jasinski, $ {G_\delta }$-covers and large thin set of real numbers, Proc. London Math. Soc. (3) 53 (1986), 518-538. MR 868457 (88a:54088)
  • [2] F. Galvin and A. W. Miller, $ \gamma $-sets and other singular sets of real line, Topology Appl. 17 (1984), 145-155. MR 738943 (85f:54011)
  • [3] J. Gerlits and Zs. Nagy, Some properties of $ C(X)$. I, Topology Appl. 14 (1982), 151-161. MR 667661 (84f:54021)
  • [4] R. Laver, On consistency of Borel's conjecture, Acta. Math. 137 (1976), 151-169. MR 0422027 (54:10019)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E50, 04A15

Retrieve articles in all journals with MSC: 03E50, 04A15

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society