If π:(X,T)→(Z,S) is a topological factor map between uniquely ergodic
topological dynamical systems, then (X,T) is called an isomorphic extension
of (Z,S) if π is also a measure-theoretic isomorphism. We consider the
case when the systems are minimal and we pay special attention to
equicontinuous (Z,S). We first establish a characterization of this type of
isomorphic extensions in terms of mean equicontinuity, and then show that an
isomorphic extension need not be almost one-to-one, answering questions of Li,
Tu and Ye.Comment: 16 page