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1999/2000 Continuity Structure of f→∪xIω(x,f) and f→{ω,f:xI}
T. H. Steele
Real Anal. Exchange 25(1): 421-428 (1999/2000).


Let the maps $\Lambda $ and $\Omega $ be defined on $C(I,I)$ so that $ f\longmapsto \Lambda (f)=\cup _{x\in I}\omega (x,f)$ and $f\longmapsto \Omega (f)=\{\omega (x,f):x\in I\}.$ We characterize those functions at which $\Lambda $ is continuous, as well as those functions at which $\Omega $ is continuous when its domain is restricted to those elements of $C(I,I)$ possessing zero topological entropy.


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T. H. Steele. "Continuity Structure of f→∪xIω(x,f) and f→{ω,f:xI}." Real Anal. Exchange 25 (1) 421 - 428, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 0937.26507
MathSciNet: MR1758898

Primary: 26A18

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

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 1 • 1999/2000
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