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2007/2008 Quasicontinuous Functions with Everywhere Discontinuous Iterates
M. Sohaib Alam, Annalisa Crannell
Real Anal. Exchange 33(1): 161-166 (2007/2008).


This paper gives examples of two quasicontinuous functions whose second iterates are discontinuous everywhere. It is well-known that every quasicontinuous function has a dense---indeed, residual---set of points of continuity; our counter-examples show that this property does not hold for compositions of such functions.


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M. Sohaib Alam. Annalisa Crannell. "Quasicontinuous Functions with Everywhere Discontinuous Iterates." Real Anal. Exchange 33 (1) 161 - 166, 2007/2008.


Published: 2007/2008
First available in Project Euclid: 28 April 2008

zbMATH: 1152.54010
MathSciNet: MR2402871

Primary: 54C08 , 54H20‎

Keywords: iteration , Quasicontinuity , quasicontinuous function

Rights: Copyright © 2007 Michigan State University Press

Vol.33 • No. 1 • 2007/2008
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