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

Lemańczyk, M.; Siemaszko, A.

doi:10.1090/S0002-9939-00-05892-5

A note on the existence of a largest topological factor with zero entropy
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by M. Lemańczyk and A. Siemaszko PDF

Proc. Amer. Math. Soc. 129 (2001), 475-482 Request permission

Abstract:

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 $\mu$, $h_\mu (\hat {S}|S)=0$. When a relative variational principle holds, $h(\hat {S})=h(S)$.

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