Remarks on small sets of reals

Author:
Tomek Bartoszynski

Journal:
Proc. Amer. Math. Soc. **131** (2003), 625-630

MSC (2000):
Primary 03E17

DOI:
https://doi.org/10.1090/S0002-9939-02-06567-X

Published electronically:
April 10, 2002

MathSciNet review:
1933355

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the Dual Borel Conjecture implies that and find some topological characterizations of perfectly meager and universally meager sets.

**1.**Tomek Bartoszynski. On perfectly meager sets. available from front.math.ucdavis.edu.**2.**Tomek Bartoszynski and Haim Judah.*Set Theory: on the structure of the real line*. A.K. Peters, 1995. MR**96k:03002****3.**Harold R. Bennett, Masami Hosobuchi, and David J. Lutzer. A note on perfect generalized ordered spaces.*Rocky Mountain J. Math.*, 29(4):1195-1207, 1999. MR**2000k:54027****4.**Timothy J. Carlson. Strong measure zero and strongly meager sets.*Proceedings of the American Mathematical Society*, 118(2):577-586, 1993. MR**94b:03086****5.**Fred Galvin and Arnold W. Miller. -sets and other singular sets of real numbers.*Topology and its Applications*, 17(2):145-155, 1984. MR**85f:54011****6.**Alexander Kechris.*Classical Descriptive Set Theory*, volume 156 of*Graduate Texts in Mathematics*. Springer Verlag, 1995. MR**96e:03057****7.**Richard Laver. On the consistency of Borel's conjecture.*Acta-Math.*, 137(3-4):151-169, 1976. MR**54:10019****8.**Arnold W. Miller. Special subsets of the real line. In K. Kunen and J. E. Vaughan, editors,*Handbook of Set Theoretic Topology*, pages 201-235. North-Holland, Amsterdam, 1984. MR**86i:54037****9.**Andrzej Nowik and Tomasz Weiss. Not every -set is perfectly meager in the transitive sense.*Proceedings of the American Mathematical Society*, 128(10):3017-3024, 2000. MR**2000m:03116****10.**Piotr Zakrzewski. Universally meager sets.*Proceedings of the American Mathematical Society*, 129(6):1793-1798, 2001. MR**2001m:03097**

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Additional Information

**Tomek Bartoszynski**

Affiliation:
Department of Mathematics and Computer Science, Boise State University, Boise, Idaho 83725

Email:
tomek@math.boisestate.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06567-X

Keywords:
Perfectly meager,
universally meager,
cardinal invariants

Received by editor(s):
July 24, 2001

Received by editor(s) in revised form:
September 19, 2001

Published electronically:
April 10, 2002

Additional Notes:
The author was partially supported by NSF grant DMS 9971282 and the Alexander von Humboldt Foundation

Communicated by:
Alan Dow

Article copyright:
© Copyright 2002
American Mathematical Society