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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
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