## Real Analysis Exchange

### Quasicontinuous Functions with a Little Symmetry Are Extendable

Francis Jordan

#### 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

https://projecteuclid.org/euclid.rae/1231187623

Mathematical Reviews number (MathSciNet)
MR1758905

Zentralblatt MATH identifier
1015.26009

#### 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

#### References

• K. Ciesielski, Set Theoretic Real Analysis, J. Appl. Anal., 3(2)(1997), 143–190. (Preprint* available\footnotePreprints marked by * are available in electronic form and can be accessed from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/homepages/kcies/STA/STA.html.)
• R. G. Gibson and T. Natkaniec, Darboux-like Functions, Real Anal. Exchange, 22(1996–97), 492–533.
• T. Natkaniec, Almost Continuity, Real Anal. Exchange, 17(1991–92), 462–520.
• H. Rosen, Darboux Quasicontinuous Functions, Real Anal. Exchange, 23(1997–98), 631–640.