Abstract
We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measureon Y the conditional entropy h(�|X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the result in (D-H) (in which the extension was principal, but not necessarily faithful).
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