Positive entropy of a homeomorphism on a compact metric space is inherited by all full-support quasifactors.
Katok,Fifty years of entropy in dynamics:1958-2007, Journal of Modern Dynamics, 2007, 1(4): 545–596
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On the entropy of processes generated by quasifactors
Positive entropy of a homeomorphism on a compact metric space is inherited by all full-support quasifactors.