## Real Analysis Exchange

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

### On Discrete Limits of Sequences of Darboux Bilaterally Quasicontinuous Functions

#### 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