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Topological size of scrambled sets for local dendrite maps
Journal article   Open access  Peer reviewed

Topological size of scrambled sets for local dendrite maps

Ghassen Askri and Issam Naghmouchi
Topology and its applications, Vol.164(1), pp.95-104
01/03/2014
DOI: https://doi.org/10.1016/j.topol.2013.12.005

Abstract

Dendrite Li–Yorke pair Local dendrite Nowhere residual Residual Scrambled set
We prove that for any local dendrite map f:X→X, any scrambled set of f is totally disconnected and hence it has empty interior. Moreover, we prove that scrambled sets are nowhere residual if the set of branch points of X is discrete, this holds in particular for Gehman dendrite.
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https://doi.org/10.1016/j.topol.2013.12.005View
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