## Real Analysis Exchange

- Real Anal. Exchange
- Volume 22, Number 1 (1996), 437-442.

### Concerning a characterization of continuity

#### Abstract

Two problems related to the characterization of continuity are discussed. In the first problem “\(f\) is almost continuous in the sense of Stallings” will be replaced with a weaker condition “\(f\) is a Darboux function” and it will be shown that the characterization of continuity remains true. Also it follows that for the classes of functions considered, “\(f\) is a Darboux function” is the weakest possible condition for which the characterization remains true. In the second problem “\(f\) is almost continuous in the sense of Stallings” will be replaced with a stronger condition “\(f\) is an extendable function”. Then it will be shown that this condition and conditions (2) and (3) are not redundant.

#### Article information

**Source**

Real Anal. Exchange, Volume 22, Number 1 (1996), 437-442.

**Dates**

First available in Project Euclid: 1 June 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.rae/1338515238

**Mathematical Reviews number (MathSciNet)**

MR1433631

**Zentralblatt MATH identifier**

0879.26011

**Keywords**

extendable function connectivity function almost continuity

#### Citation

Gibson, Richard G. Concerning a characterization of continuity. Real Anal. Exchange 22 (1996), no. 1, 437--442. https://projecteuclid.org/euclid.rae/1338515238