Continuity Structure of f→∪_x∈Iω(x,f) and f→{ω,f:x∈I}

Steele, T. H.

Real Anal. Exchange, Tome 25 (1999) no. 1, p. 421-428 / Harvested from Project Euclid

Résumé

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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Publié le : 1999-05-15
Classification:  $\omega $-limit set,  topological entropy,  26A18