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