Real Analysis Exchange

Unilateral I-approximate Limits of Real Functions

Rafał Zduńczyk

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Abstract

We consider sets of generalized discontinuity of real functions with respect to local systems fulfilling the intersection condition. We give a sufficient condition for countability of such set. This result is used to prove its $\mathbb{I}$-density analogue.

Article information

Source
Real Anal. Exchange Volume 34, Number 1 (2008), 105-114.

Dates
First available in Project Euclid: 19 May 2009

Permanent link to this document
http://projecteuclid.org/euclid.rae/1242738923

Mathematical Reviews number (MathSciNet)
MR2527125

Subjects
Primary: 26A03,26A15 26A03: Foundations: limits and generalizations, elementary topology of the line

Keywords
local system intersection condition I-approximate continuity I-density topology

Citation

Zduńczyk, Rafał. Unilateral I -approximate Limits of Real Functions. Real Anal. Exchange 34 (2008), no. 1, 105--114. http://projecteuclid.org/euclid.rae/1242738923.


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References

  • Krzysztof Ciesielski, Lee Larson, and Krzysztof Ostaszewski, $\mathcal I$-density Continuous Functions, Mem. Amer. Math. Soc., 107(515) (1994).
  • Tomasz Filipczak, Intersection conditions for some density and I-density local systems, Real Anal. Exchange, 15(1) (1989-90), 170–192.
  • Marcin Grande, On the sums of unilaterally approximately continuous and approximately jump functions, Real Anal. Exchange, 28(2) (2002/2003), 623–630.
  • Ewa Łazarow and Władysław Wilczyński, I-Approximate derivatives, Radovi Matematički, 5 (1989), 15–27.
  • Brian Thomson, Real Functions, Lecture Notes in Math., 1170 Springer-Verlag, New York, 1980.
  • Władysław Wilczyński, Separate I-approximate continuity implies the Baire property, Zeszyty Naukowe Politechniki Śląskiej, Seria: Matematyka–Fizyka, 48(853) (1986).