## Real Analysis Exchange

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

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

#### 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

**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