Real Analysis Exchange

Residuality of families of Fσ sets.

Shingo Saito

Full-text: Open access

Abstract

We prove that two natural definitions of residuality of families of $\mathcal{F}_\sigma$ sets are equivalent. We make use of the Banach-Mazur game in the proof.

Article information

Source
Real Anal. Exchange, Volume 31, Number 2 (2005), 477-487.

Dates
First available in Project Euclid: 10 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184104040

Mathematical Reviews number (MathSciNet)
MR2265789

Zentralblatt MATH identifier
1098.54028

Subjects
Primary: 54B20: Hyperspaces
Secondary: 54E52: Baire category, Baire spaces

Keywords
Residuality $\mathcal{F}_{\sigma}$ set Banach-Mazur game

Citation

Saito, Shingo. Residuality of families of F σ sets. Real Anal. Exchange 31 (2005), no. 2, 477--487. https://projecteuclid.org/euclid.rae/1184104040


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References

  • John C. Oxtoby, The Banach-Mazur Game and Banach Category Theorem, Contributions to the Theory of Games, vol. 3, Annals of Mathematics Studies 39 (1957), 159–163, Princeton University Press.
  • Robert R. Phelps, Convex Functions, Monotone Operators and Differentiability, second edition, Lecture Notes in Mathematics 1364 (1993), Springer-Verlag.
  • Tudor Zamfirescu, How Many Sets Are Porous?, Proceedings of the American Mathematical Society 100 (1987), vol. 2, 383–387.