## Real Analysis Exchange

### On Discrete Limits of Sequences of Bilaterally Quasicontinuous, Baire 1 Functions

Zbigniew Grande

#### Abstract

In this article we show that for the discrete limit $f$ of sequence of bilaterally quasicontinuous Baire 1 functions the complement of the set of all points at which $f$ is bilaterally quasicontinuous and has Darboux property, is nowhere dense. Moreover, a construction is given of a bilaterally quasicontinuous function which is the discrete limit of a sequence of Baire 1 functions, but is not the discrete limit of any sequence of bilaterally quasicontinuous Baire 1 functions.

#### Article information

Source
Real Anal. Exchange, Volume 26, Number 1 (2000), 429-436.

Dates
First available in Project Euclid: 2 January 2009

https://projecteuclid.org/euclid.rae/1230939172

Mathematical Reviews number (MathSciNet)
MR1825522

Zentralblatt MATH identifier
1009.26006

#### Citation

Grande, Zbigniew. On Discrete Limits of Sequences of Bilaterally Quasicontinuous, Baire 1 Functions. Real Anal. Exchange 26 (2000), no. 1, 429--436. https://projecteuclid.org/euclid.rae/1230939172

#### References

• Bruckner A.M.; Differentiation of real functions, Lectures Notes in Math. 659, Springer-Verlag, Berlin 1978.
• Bruckner A.M. and Ceder J.; Darboux continuity Jber. Deut. Math. Ver. 67 (1965), 93–117.
• Császár A. and Laczkovich M.; Discrete and equal convergence, Studia Sci. Math. Hungar. 10 (1975), 463–472.
• Grande Z.; On discrete limits of sequences of approximately continuous functions and $T_{ae}$-continuous functions, to appear.
• Grande Z.; On discrete limits of sequences of Darboux bilaterally quasicontinuous functions, to appear.
• Grande Z. and Strońska E.; Some remarks on disrete and uniform convergence, to appear.
• Kempisty S.; Sur les fonctions quasi-continues, Fund. Math. 19 (1932), 184–197.
• Neubrunn T.; Quasi-continuity, Real Anal. Exch. 14 No.2 (1988–89), 259–306.