  If $\pi:(X,T)\to(Z,S)$ is a topological factor map between uniquely ergodic
topological dynamical systems, then $(X,T)$ is called an isomorphic extension
of $(Z,S)$ if $\pi$ 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.
