Real Analysis Exchange
- Real Anal. Exchange
- Volume 33, Number 1 (2007), 161-166.
Quasicontinuous Functions with Everywhere Discontinuous Iterates
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.
Real Anal. Exchange, Volume 33, Number 1 (2007), 161-166.
First available in Project Euclid: 28 April 2008
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Crannell, Annalisa; Alam, M. Sohaib. Quasicontinuous Functions with Everywhere Discontinuous Iterates. Real Anal. Exchange 33 (2007), no. 1, 161--166. https://projecteuclid.org/euclid.rae/1209398386