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A note on the existence of a largest topological factor with zero entropy

Authors: M. Lemanczyk and A. Siemaszko
Journal: Proc. Amer. Math. Soc. 129 (2001), 475-482
MSC (2000): Primary 37B40
Published electronically: July 27, 2000
MathSciNet review: 1800236
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Given a topological system $T$ on a $\sigma$-compact Hausdorff space and its factor $S$ we show the existence of a largest topological factor $\hat{S}$ containing $S$ such that for each $\hat{S}$-invariant measure $\mu$, $h_\mu(\hat{S}\vert S)=0$. When a relative variational principle holds, $h(\hat{S})=h(S)$.

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Additional Information

M. Lemanczyk
Affiliation: Faculty of Mathematics and Computer Science, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

A. Siemaszko
Affiliation: Department of Applied Mathematics, Olsztyn University of Agriculture and Technology, Oczapowskiego 1, 10-957 Olsztyn-Kortowo, Poland

Keywords: Topological entropy, relative Pinsker factor
Received by editor(s): April 22, 1999
Published electronically: July 27, 2000
Communicated by: Michael Handel
Article copyright: © Copyright 2000 American Mathematical Society

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