## Real Analysis Exchange

### Concerning a characterization of continuity

Richard G. Gibson

#### 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

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

Mathematical Reviews number (MathSciNet)
MR1433631

Zentralblatt MATH identifier
0879.26011

#### Citation

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

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