Real Analysis Exchange

On Discrete Limits of Sequences of Darboux Bilaterally Quasicontinuous Functions

Zbigniew Grande

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Abstract

In this article we show that a function $f$, such that the complement of the set of points at which $f$ has the Darboux property and is bilaterally quasicontinuous is nowhere dense, must be the discrete limit of a sequence of bilaterally quasicontinuous Darboux functions. Moreover, there is given a construction of a function that is the discrete limit of a sequence of bilaterally quasicontinuous Darboux functions and which does not have a local Darboux property on a dense set.

Article information

Source
Real Anal. Exchange, Volume 26, Number 2 (2000), 727-734.

Dates
First available in Project Euclid: 27 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1214571363

Mathematical Reviews number (MathSciNet)
MR1844389

Zentralblatt MATH identifier
1024.26002

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} 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 26A99: None of the above, but in this section

Keywords
Discrete convergence quasicontinuity bilateral quasicontinuity Darboux property

Citation

Grande, Zbigniew. On Discrete Limits of Sequences of Darboux Bilaterally Quasicontinuous Functions. Real Anal. Exchange 26 (2000), no. 2, 727--734. https://projecteuclid.org/euclid.rae/1214571363


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References

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