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A mixing completely scrambled system exists
Published online by Cambridge University Press: 04 May 2017
Abstract
We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that, for any integer $n\geq 1$, there is a continuum of topological dimension $n$ supporting a transitive completely scrambled homeomorphism and an $n$-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15-year-old open problem.
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- © Cambridge University Press, 2017
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