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1998/1999 The Set of Continuous Functions with Zero Topological Entropy
T. H. Steele
Real Anal. Exchange 24(2): 821-826 (1998/1999).


Let $I=[0,1]$. We show that those functions in $C(I,I)$ possessing zero topological entropy form a nowhere dense perfect subset of the continuous self maps of the interval. We also show that every function with zero topological entropy that possesses an infinite $\omega $-limit set is the uniform limit of functions having only finite $\omega $-limit sets.


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T. H. Steele. "The Set of Continuous Functions with Zero Topological Entropy." Real Anal. Exchange 24 (2) 821 - 826, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 28 September 2010

zbMATH: 0962.54032
MathSciNet: MR1704754

Primary: 54H20‎

Keywords: $\omega$-limit set , Continuous function , topological entropy

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
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