Real Analysis Exchange

Quasicontinuous Functions with Everywhere Discontinuous Iterates

M. Sohaib Alam and Annalisa Crannell

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 33, Number 1 (2007), 161-166.

Dates
First available in Project Euclid: 28 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1209398386

Mathematical Reviews number (MathSciNet)
MR2402871

Zentralblatt MATH identifier
1152.54010

Subjects
Primary: 54C08: Weak and generalized continuity 54H20: Topological dynamics [See also 28Dxx, 37Bxx]

Keywords
iteration quasicontinuity quasicontinuous function

Citation

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


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