For minimal systems, frequent stability is equivalent to the maximal equicontinuous factor being almost one-to-one, and diam-mean equicontinuity is equivalent to that factor being regular.
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Mean equicontinuity, almost automorphy and regularity
For minimal systems, frequent stability is equivalent to the maximal equicontinuous factor being almost one-to-one, and diam-mean equicontinuity is equivalent to that factor being regular.