Real Analysis Exchange

Quasicontinuous Functions with a Little Symmetry Are Extendable

Francis Jordan

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Abstract

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

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

Dates
First available in Project Euclid: 5 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1231187623

Mathematical Reviews number (MathSciNet)
MR1758905

Zentralblatt MATH identifier
1015.26009

Subjects
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]

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

Citation

Jordan, Francis. Quasicontinuous Functions with a Little Symmetry Are Extendable. Real Anal. Exchange 25 (1999), no. 1, 485--488. https://projecteuclid.org/euclid.rae/1231187623


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References

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