Real Analysis Exchange

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

Zbigniew Grande

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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

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230939172

Mathematical Reviews number (MathSciNet)
MR1825522

Zentralblatt MATH identifier
1009.26006

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}

Keywords
Baire 1 class bilateral quasicontinuity discrete convergence Darboux property

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


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References

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