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Let (X, T) be a metrizable minimal flow. We show that a homomorphism X -) Y, which is regular, and PI can be decomposed as X a Z ) Y., 7r = p o a, where p is proximal and a is a compact group extension. In particular, assuming further that T is abelian and taking Y to be the trivial one point flow, we find that a metric regular PI flow is a compact group rotation.

Regular PI metric flows are equicontinuous