Real Analysis Exchange

Concerning a characterization of continuity

Richard G. Gibson

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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

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

First available in Project Euclid: 1 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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}

extendable function connectivity function almost continuity


Gibson, Richard G. Concerning a characterization of continuity. Real Anal. Exchange 22 (1996), no. 1, 437--442.

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