Real Analysis Exchange

Quasicontinuous Functions with a Little Symmetry Are Extendable

Francis Jordan

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It is shown that if a function $f\colon\real\to\real$ is quasicontinuous and has a graph which is bilaterally dense in itself, then $f$ must be extendable to a connectivity function $F\colon\real^2\to\real$ and the set of discontinuity points of $f$ is $f$-negligible. This improves a result of H.~Rosen. A similar result for symmetrically continuous functions follows immediately.

Article information

Real Anal. Exchange, Volume 25, Number 1 (1999), 485-488.

First available in Project Euclid: 5 January 2009

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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}
Secondary: 54C30: Real-valued functions [See also 26-XX]

symmetrically continuous functions extendable functions quasicontinuous functions peripherally continuous functions Darboux functions


Jordan, Francis. Quasicontinuous Functions with a Little Symmetry Are Extendable. Real Anal. Exchange 25 (1999), no. 1, 485--488.

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