Real Analysis Exchange

Continuity Points of Typical Bounded Functions

Shingo Saito

Full-text: Open access

Abstract

Kostyrko and Šalát showed that if a linear space of bounded functions has an element that is discontinuous almost everywhere, then a typical element in the space is discontinuous almost everywhere. We give a topological analogue of this theorem and provide some examples.

Article information

Source
Real Anal. Exchange, Volume 34, Number 1 (2008), 249-254.

Dates
First available in Project Euclid: 19 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1242738936

Mathematical Reviews number (MathSciNet)
MR2527138

Zentralblatt MATH identifier
1181.26007

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
Secondary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]

Keywords
continuity points typical functions

Citation

Saito, Shingo. Continuity Points of Typical Bounded Functions. Real Anal. Exchange 34 (2008), no. 1, 249--254. https://projecteuclid.org/euclid.rae/1242738936


Export citation

References

  • A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math., 156, Springer-Verlag, New York, 1995.
  • P. Kostyrko and T. Šalát, On the structure of some function space, Real Anal. Exchange, 10(1) (1984–85), 188–193.
  • J. C. Oxtoby, Measure and Category, $2^\text{nd}$ ed., Grad. Texts in Math., Springer-Verlag, New York, 1980.