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1997/1998 Darboux Quasicontinuous Functions
Harvey Rosen
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Real Anal. Exchange 23(2): 631-640 (1997/1998).


Let \(C(f)\) denote the set of points at which a function \(f:I\to I\) is continuous, where \(I=[0,1]\). We show that if a Darboux quasicontinuous function \(f\) has a graph whose closure is bilaterally dense in itself, then \(f\) is extendable to a connectivity function \(F: I^2\to I\) and the set \(I\setminus C(f)\) of points of discontinuity of \(f\) is \(f\)-negligible. We also show that although the family of Baire class 1 quasicontinuous functions can be characterized by preimages of sets, the family of Darboux quasicontinuous functions cannot. An example is found of an extendable function \(f: I\to \mathbb{R}\) which is not of Cesaro type and not quasicontinuous.


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Harvey Rosen. "Darboux Quasicontinuous Functions." Real Anal. Exchange 23 (2) 631 - 640, 1997/1998.


Published: 1997/1998
First available in Project Euclid: 14 May 2012

zbMATH: 0943.26010
MathSciNet: MR1639996

Primary: 26A15
Secondary: ‎54C30

Keywords: {Baire 1 function} , {Cesaro type function} , {characterizable by preimages} , {Darboux function} , {extendable connectivity function} , {quasicontinuous function}

Rights: Copyright © 1999 Michigan State University Press

Vol.23 • No. 2 • 1997/1998
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